M. Palmer enters the game and replaces R. Williams.
Make that a double change for Rotherham, as Palmer is on for Williams. Both managers have now made all three subs available to them.
89'
R. Wood enters the game and replaces Z. Vyner.
Warne brings on Wood in place of Vyner for the final minute or so of the match, possibly to eat up some more seconds.
87'
SAVE! Well if nothing else, Rotherham can at least say they managed a shot on target today! Forde does well to cut the ball back for Smith, but the shot is a little too central and Ederson is equal to it, keeping his clean sheet intact.
85'
L. Sané has scored a goal for Manchester City! Assist by İ. Gündoğan.
Four assists for Gundogan, who has been superb all match. Just like the assist for Mahrez's goal, the Germany midfielder played a quick one-two with his team-mate - Sane on this occasion - and Rotherham could not get anywhere near the ball.
GOOOOAAALLL! MAN CITY 7-0 ROTHERHAM! The seventh goal arrives with five minutes still to play at the Etihad Stadium, matching Tottenham's result against Tranmere a couple of days ago. Gundogan is again involved, exchanging passes with Sane, who gets away from Ajayi and blasts the ball down the middle from outside the box. A deflection helps it over Rodak.
84'
City are simply toying with their opponents in the closing stages of the match. The incredible thing is, the home side have not even really had to hit their full stride today.
82'
One more goal for City would make this Rotherham's outright heaviest FA Cup defeat - something to aim for in the remaining eight minutes, then! Guardiola's men have not exactly taken their foot off the gas since scoring their sixth goal.
80'
Rotherham's best moments today have come when they have launched the ball into the box, putting City's defenders and goalkeepers under a bit of pressure. The Championship strugglers have not looked like scoring, though, and they now have just 10 minutes to bag a consolation.
78'
N. Otamendi has scored a goal for Manchester City! Assist by İ. Gündoğan.
Gundogan has shown exactly why he is so highly-rated by Guardiola with his hat-trick of assists. This latest one came from a right-sided corner, which was crying out to be attacked by Otamendi - and attack it he did.
GOOOAALLLL!! MAN CITY 6-0 ROTHERHAM! Gundogan completes his hat-trick of assists by sending a corner towards the front post, where Otamendi - far from a regular goalscorer - is waiting to power the ball past Rodak with his head.
77'
POWERFUL STRIKE! Walker certainly knows how to hit the ball, and this shot from range moves all over the place. Rodak watches it all the way and parries it to safety, keeping the scoreline at 5-0 for now.
Minute
Description
75'
Danilo enters the game and replaces J. Stones.
Stones, one of three players to start both the Liverpool match and this one, is taken off with 15 minutes to play. Danilo will slot into the backline.
74'
S. Raggett enters the game and replaces J. Taylor.
Raggett is brought on for Taylor in the visiting side's first change of the match. A defender for a winger, which says it all.
73'
R. Mahrez has scored a goal for Manchester City! Assist by İ. Gündoğan.
Gundogan has his second assist of the match, showing good awarness once again to complete the one-two with Mahrez, who finishes off this latest flowing move.
GOOAAALLL! MAN CITY 5-0 ROTHERHAM! Mahrez adds his name to the scoresheet with a good finish through the legs of Rodak. The Algeria winger exchanges passes with Gundogan and keeps his composure with just the goalkeeper to beat. Rotherham cannot deal with their opponents' quick passing.
71'
CLAWED AWAY! Rodak makes a last-ditch save by hooking the ball off his goal line. Vaulks made contact with the corner and it would have been an own goal if not for his goalkeeper's intervention.
69'
Taylor's eyes light up as he charges through, with just Ederson to beat. However, the offside flag was raised to deny the winger a shot at goal. A little over 20 minutes to go here.
67'
P. Sandler enters the game and replaces K. De Bruyne.
Sandler is brought on for his Man City debut, taking over from De Bruyne. The man making way has been brilliant today, despite missing another couple of weeks through injury.
65'
SAVE! Mahrez slots the ball through for Jesus, who cuts inside and gets a shot on target. The ball appeared to get stuck under the Brazil striker's feet, and Rodak was always expected to make the save.
63'
Mahrez takes range from close to 30 yards, sending the ball well over the target. The Algeria winger has been on the periphery of things today.
61'
Ajayi has actually been one of Rotherham's better performers today, despite scoring an own goal and conceding three more, as he gets in the way to prevent Jesus from converting De Bruyne's cross.
59'
The home side are going through the motions as we approach the hour mark. The game was put to bed thanks to their quickfire goals at the end of the first half, and they have since gone on to add a fourth through Jesus.
57'
L. Sané enters the game and replaces R. Sterling.
Sane will be given a little over half an hour to add his name to the scoresheet, taking over from Sterling out wide. Guardiola clearly has no sympathy for the visitors.
56'
Things are not going to get any easier for Rotherham, as Sane appears as though he is about to enter the fray. Will it be Sterling or Mahrez who makes way?
54'
City are cruising their way through this third-round tie. Guardiola will surely consider making a few changes in the remaining 35 minutes or so to give some of his regulars a bit of a breather.
52'
Gabriel Jesus has scored a goal for Manchester City! Assist by R. Sterling.
Rotherham do not really look as though they are interested in scoring a consolation. Instead, the visitors are dropping deeper and deeper and are desperately trying to keep their opponents out.
GOOOALLL!! MAN CITY 4-0 ROTHERHAM! With seven minutes of the second half played, Jesus gets the goal that he was desperately after. Sterling creates it by powering past Vyner down City's left and teeing up his team-mate for the simplest of finishes from a few yards out.
Make that 101 combined goals and assists in a Man City shirt for Sterling. The England winger left Vyner for dead with his pace and opted to square the ball for Jesus rather than going for goal himself.
50'
De Bruyne sends in a phenomenal cross from the right that Rodak does well to push aside. The home side are only in about second gear at the moment but they look as though they could add a few goals to their tally at this rate.
47'
Jesus could do with a goal in this second half to boost his confident. Ajayi comes out on top in their first tussle of the second half, showing far too much strength for the City striker.
46'
Man City, boasting a three-goal lead at the start of the second half, get us back underway at the Etihad Stadium.
45' +3
HALF-TIME: MAN CITY 3-0 ROTHERHAM
45' +1
S. Ajayi is unfortunate, scores an own goal!
GOOOAALLL!! MAN CITY 3-0 ROTHERHAM! The visitors have completely fallen apart over the past few minutes. Mahrez has a back-post header saved by Rodak, but the Rotherham keeper is unable to prevent Ajayi from scoring an own goal. Walker wins a header high up the pitch and exchanges passes with Mahrez, before sending in a dangerous cross that is turned in by Ajayi, who had Sterling breathing down his neck.
43'
P. Foden has scored a goal for Manchester City! Assist by İ. Gündoğan.
GOOOAAALLL!! MAN CITY 2-0 ROTHERHAM! The home side score what could well be a killer second goal, and it is Foden who scores it for only his second goal in senior football. It was a bit of a fluke, in truth, as the youngster miscontrols Gundogan's ball over the top, knocking it against his knee with a poor first touch, but it trickles past Rodak.
Great vision from Gundogan, who clips the ball over Rotherham's deep defence right into the path of Foden. The finish may have been a fluke but there was nothing lucky about the assist.
41'
Rotherham boss Warne will be a happy man if his side can hold on for the next four minutes, plus added time, and go into the break just a goal down. United are dropping deeper and deeper and there is a sense that a second City goal is on its way.
39'
City, for all their possession, have only managed one shot on target in the first half. The English champions have created some good chances, but Jesus is having a bit of a nightmare up top, meaning that the game is far from over as we approach the midway point.
37'
Vyner sends a teasing cross into the six-yard box, which Ederson thinks he can get to. The Brazil goalkeeper did not make the contact he was after, taking out Taylor and Stones in the process, but it was enough to prevent a Rotherham player from getting on the end of the delivery.
35'
R. Sterling gets yellow.
Goalscorer Sterling joins Wiles in the referee's book for a strong challenge on Smith. The England winger argues that he got some of the ball, but you always run the risk of being cautioned when you lunge in from the side.
33'
ANOTHER CHANCE FOR JESUS! The Brazil striker is not exactly a man full of confidence at the moment, miscuing his close-range attempt following some good build-up play from Mahrez and De Bruyne.
31'
Seconds after that howler from Ederson, City get up the pitch and Ederson heads over the crossbar. Not as good as his two earlier opportunities, but that is a half-chance at the very least.
30'
HOWLER FROM EDERSON! Stones bails out his goalkeeper with his quick reaction in front of goal. Ederson is caught in possession by Forde, who is closing down the goalkeeper at every opportunity. Stones was first to the loose ball, though, preventing what would have been a simple tap-in.
28'
Rotherham have done well since falling behind to Sterling's 12th-minute strike. City are probing away down the flanks and putting together some promising attacks, but the Championship visitors are standing firm at the back.
26'
Sterling shows good strength to get to the byline, before Jesus and then Zinchenko take over. Rotherham defend the danger well, though, with Ajayi hitting the ball out of play off Zinchenko's legs.
25'
Forde has clearly been told to put Ederson under pressure when the goalkeeper is on the ball, but he goes a little too far by lunging in on his opponent. The referee David Coote gives the Rotherham player a warning.
24'
B. Wiles gets yellow.
Wiles is the first player to be cautioned today for tug on Sterling's shirt. The England winger is looking very lively on the left flank and already has a goal to his name.
22'
Guardiola's men are starting to knock on the door for a second goal, which would surely kill off the tie. As long as it remains at just 1-0, United have a slim chance of claiming a draw - or indeed better.
20'
City completely dominated the opening 12 minutes of the match and were good value for their goal when it arrived via Sterling. Since then, though, the hosts have not looked anywhere near as dangerous, even if they have seen plenty of the ball.
18'
Play finally resumes at the Etihad Stadium following a stoppage of around three minutes. The official taking over had to get wired up so that he can communicate with the referee. The atmosphere has gone rather flat all of a sudden as a result of the break in play.
16'
There is a short stoppage in play as one of the linesmen has picked up an injury and needs to be replaced. That may work against Rotherham as they have enjoyed a good spell since falling behind.
14'
BETTER FROM ROTHERHAM! Seconds after falling behind, Rotherham put together their first real attacking move of the match. The ball falls to Ajayi from a set-piece, but his deflected shot flies wide of the near post. Ederson probably would have got there had he needed to.
12'
R. Sterling has scored a goal for Manchester City! Assist by K. De Bruyne.
De Bruyne has taken no time at all to get back into the flow of things. The Belgium playmaker could have gone for goal himself after being picked out by Sterling on the edge of the box, but he instead played the return pass and his team-mate did the rest.
GOOOAAALLL!! MAN CITY 1-0 ROTHERHAM! The home side score the goal that their early dominance deserves. De Bruyne and Sterling exchange passes and the latter shifts the ball onto his right, before calmly guiding it past Rodak.
11'
SAVE! Rodak pushes Mahrez's shot wide of goal and City are unable to make the most of the corner. The home side have had 73% of the ball so far - it feels like a lot more!
9'
CHANCE! It has been a constant bombardment from the Premier League side in the opening 10 minutes. Jesus, having already missed one big chance, squanders another as he fails to get anything on Mahrez's cross when picked out five yards from goal. Did he take his eyes off the ball?
7'
The home side are looking very sharp, with Mahrez playing a ball towards the back post but getting a little too much on it - Zinchenko could only watch it run out of play. Rotherham have barely had a touch of the ball so far.
5'
Rodak is quickly off his line to get to the ball before Sterling. City are in the mood for goals today, and they could easily have had one early on through that Jesus chance.
4'
Rotherham are picked apart for the second time in the opening four minutes, as the ball is played through for Sterling. Ajayi produces a good challenge, but it almost works against him as the ball ricochets off Sterling and into the side-netting.
2'
OFF THE BAR! Ninety seconds on the clock and City should be ahead. De Bruyne gets to the byline and clips the ball towards the back post, where Jesus is waiting to meet it. The Brazil striker, perhaps put off by the contact from Vyner, can only skim the crossbar with his header from close range.
1'
Rotherham get this FA Cup third-round tie underway!
Hello and welcome to our live coverage of the FA Cup third-round tie between Manchester City and Rotherham United at the Etihad Stadium.
Premier League champions Man City are the favourites of many to go all the way and lift the FA Cup at Wembley in May, eight years after last managing the feat with a Yaya Toure-inspired victory over Stoke City. Pep Guardiola’s men revived their top-flight campaign with a crucial 2-1 win over leaders Liverpool in midweek, and now focus turns to this first of two domestic cup matches in the space of three days as they play host to Championship strugglers Rotherham.
MAN CITY XI (4-3-3): Ederson; Kyle Walker, John Stones, Nicolas Otamendi, Oleksandr Zinchenko; Kevin De Bruyne (c), Ilkay Gundogan, Phil Foden; Riyad Mahrez, Gabriel Jesus, Raheem Sterling
Man City subs: Philippe Sandler, Aymeric Laporte, Bernardo Silva, Arijanet Muric, Fernandinho, Leroy Sane, Danilo
ROTHERHAM XI (4-4-1-1): Marek Rodak; Zak Vyner, Semi Ajayi, Clark Robertson, Joe Mattock; Jon Taylor, Will Vaulks (c), Ryan Williams, Anthony Forde; Ben Wiles; Michael Smith
Rotherham subs: Joe Newell, Sean Raggett, Matthew Palmer, Lewis Price, Billy Jones, Richard Wood
The two teams are now out on the field at the Etihad Stadium and we are moments away from kick-off. Man City have returned to form over the past week with league wins over Southampton and Liverpool, while Rotherham also head into this match on a high as they beat Preston on New Year's Day to move three points clear of the Championship relegation zone. Focus for both sides now switches to domestic cup duties, with a place in round four up for grabs.
Man City have as good as booked their place in the fourth round of the FA Cup, having taken a three-goal lead into half-time against Rotherham. The Championship side held firm for 20 minutes after falling behind to a Sterling strike, but a close-range finish from Foden and an Ajayi own goal late in the half has moved the competition favourites out of sight.
It may well be a case of damage limitation for Rotherham in the second half after completely crumbling in the final few minutes of the first period. The second-tier strugglers were always going to have their work cut out today, especially with Guardiola naming a strong starting line-up, and the best they can hope for now is a consolation in the remaining 45 minutes.
Thanks for joining our coverage today. Until next time, goodbye!
Guardiola's men have now won three matches in a row in all competitions and have plenty of momentum on their side ahead of Wednesday's EFL Cup semi-final first-leg clash with Burton Albion here. Rotherham, meanwhile, must pick themselves up as they have a Championship relegation showdown with Ipswich Town to prepare for in six days' time.
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