The reigning Premier League champions largely dominated proceedings at the Etihad Stadium. For their part, Burnley started the game off brightly, showing their intention to attack - with Maxwel Cornet proving to be a consistent threat throughout the game, especially on the break.
The superior technical ability of the men in blue was evident, though. And on the 12th minute, Bernardo Silva put his team in front with a tap-in following a save by Nick Pope from a shot by Phil Foden.
The Clarets didn't sit back when out of possession and pressed City's back-line hard when they had the opportunity, almost securing an equaliser when Brownhill shot just wide of the left post.
Sean Dyche's team may well feel hard-done by, when at the end of the first-half, Aymeric Laporte made a jumping tackle on Dwight McNeil with both feet outstretched, but only saw a yellow card.
However. it was Pep Guardiola's side who had enough chances to put themselves out of sight in the second-half, and were eventually able to score that second goal courtesy of Kevin De Bruyne's left foot.
Here's how City Xtra rated the players in this hard-fought win on Saturday-
Zack Steffen - 8
The USMNT star had a great game on his first Premier League appearance of the season, keeping City in the lead by saving a 1v1 shot after Cornet found himself in front of goal. The 26-year-old goalkeeper made the right decisions when he had to, and did about as much as he could to stick a claim in for being City's number-one pick.
Joao Cancelo - 7.5
When his teammates had the ball, Cancelo was free to roam forward, getting on the end of few crosses from De Bruyne in the opposition box. The Portuguese should have put City 2-0 up in the first-half but for a Nick Pope save after shooting from close-range.
John Stones - 8
It's hard to believe this was Stones' first appearance of the season for City, considering how essential he was to their title win last season. The Yorkshire native put in a solid defensive performance against the team from Lancashire, making some well-timed tackles which kept his team in front.
Aymeric Laporte - 7
Had almost as good a game as Stones, staying positionally strong to prevent crosses during Burnely's moments in the ascendency. The 27-year-old made an unnecessary challenge on McNeil just before the end of the first-half, which saw him booked.
Nathan Aké - 6.5
A surprise edition to the starting lineup, playing at left-back, where he didn't look entirely comfortable, particularly going forward. Oftentimes seemed a little like a spare-part, but didn't do anything to warrant a poor rating.
Rodrigo - 7.5
After putting in three solid career-defining performances prior to the international break, this was more of a quiet game for the Spaniard. It was still a good outing for Rodri, who was strong in the middle of the park, tackling well and winning aerial duals when needed.
Kevin De Bruyne - 8
It's fair to say that De Bruyne hasn't been firing on all cylinders recently. Even not at his absolute best, the Belgian still managed to play some fantastic crosses into the box, and scored City's second with a missile of a shot with his left foot, smashing the back of the net.
Bernardo Silva - 8.5 (MOTM)
Another stellar game from the Portuguese which will have City fans across the world hoping no-one comes in for him over the next few transfer windows. Had the positional awareness to be there for the opener, following a rebound from Foden's shot. The midfielder combined brilliantly with players across all areas of the pitch, showing just how essential he is to Guardiola's system.
Riyad Mahrez - 7
After Gabriel Jesus featured for Brazil on Friday evening, this was Mahrez's chance to cement himself back into Guardiola's starting XI. Despite the Algerian usually loving this fixture, he was far from his ruthless best against Sean Dyche's men.
Phil Foden - 7.5
After starring for England during the international break, Foden ran the show on the left side for his boyhood club. The 21 year-old used his pace and technical ability to get behind Burnley's back line, causing threats with shots and passes across the face of goal. Found himself through on goal on a couple of occasions, but was muscled off the ball and ushered away from being able to shoot.
Raheem Sterling - 6.5
After all the recent transfer speculation surrounding Sterling due to his lack of starts for City this season, the England international was presented with his chance. Starting down the middle, the forward didn't see a lot of the ball in the first-half, with Foden, Mahrez, and Cancelo the preferred choice of target-men. After the break, Sterling moved out to the left where he was more active and influential in the game, but never really left his mark on the tie.
Ruben Dias - 6
Came on for Laporte around the with less than 30 minutes left on the clock. Helped keep a clean sheet after Burnley took control of the clash
Fernandinho - N/A
No time to mark.
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