Arsenal looked to have secured a point, only for Rodri to stab the ball home from close range in the 93rd minute to help the Sky Blues claim an 11th successive league win.
Sportsmail's Nick Callow has rated how the players performed during the Saturday afternoon encounter.
Ramsdale: Another confident display from the England international, who had a surprisingly quiet day until City got a penalty. 6
Tomiyasu: Back from Covid and all over Sterling from the start. Got forward well too. Arsenal have a really good right-back in the Japan international. 7
White: So comfortable on the ball and solid in the tackle. Played some excellent passes from the back too. 7
Gabriel: Ruined what had been an excellent performance by getting himself sent off with two senseless bookings. 4
Arsenal defender Gabriel had a day to forget as he was shown a red card by Stuart Attwell
Tierney: Ever reliable left-back, who also kept Mahrez honest with his attacking runs down the wing. Great assist for Saka's opener. 7
Partey: Finally showing the form that made him one of the most respected midfielders in Europe when he was at Atletico Madrid. Arsenal will miss him more than most when he goes to AFCON. 8
Thomas Partey proved why Arsenal brought him to the Emirates with a stellar performance
Xhaka: Strangely measured from the Swiss midfielder who has so often lost his head and his feet in big matches such as this. Passed well and kept his emotions in check. Conceded a debateable penalty. 6
Odegaard: Lacked his usual touch and control at times but made up for it with his intelligent runs and pressing when Arsenal needed the ball back. 6
Saka: Showed once again he can be a very good player at the highest level as he dominated the right wing three years to the day since his Premier League debut. 8
Bukayo Saka (right) gave the Arsenal the lead on 31 minutes with a well taken finish
Martinelli: One of Arsenal's more dangerous players going forward. Too much pace and skill for City at times but lacked a killer finish. No wonder Smith Rowe is stuck on the bench. 8
Lacazette: Tireless tackling and chasing from the French striker. Held the forward line together so well and tried to keep his players calm when the referee went on a booking spree. 6
Subs: Holding (replaced Odegaard 63) 6
Smith Rowe - (replaced Lacazette 71) 6
Elneny - (replaced Saka 84) N/A
Subs not used: Leno, Smith Rowe, Maitland-Niles, Holding, Soares, Pepe, Tavares, Lokonga.
Ederson: Dressed head to toe in luminous yellow like a steward, there was no escaping the Brazilian who played his sweeper-keeper role so well. Brilliantly timed tackle to deny Odegaard. 7
Cancelo: Such a good player, but has played better. Struggled against Martinelli's pace. Finished strongly once Arsenal were down to ten men. 6
Dias: A dominant presence in defence and attack. Should have headed in from a great Sterling cross, but, more importantly for City, was faultless at the back. 7
Ruben Dias helped marshal the back four and was a key figure alongside Aymeric Laporte
Laporte: Has become such a key figure in this excellent City defence and hardly put a foot wrong once again. 7
Ake: So quick and confident. Almost but not quite honours even in his one-on-one battle with winger Bukayo Saka. Brilliant goal-line clearance. 6
Rodri: Mopped up so much in front of the City back line. What a tackler! Possibly the best player in his position in the Premier League. Crucial goal. 8
Rodri fired past Aaron Ramsdale on 93 minutes to secure the three points for Manchester City
De Bruyne: Back to his best in recent weeks and no change here as he pinged passes with precision and pressed relentlessly when Arsenal had the ball. 7
Silva: A relatively quiet game until he came to life in the penalty area to win his side a penalty. 6
Sterling: One of City's better players when Arsenal were on top and posed the greatest attacking threat with his dribbling skills and direct approach. 6
Mahrez: A poor game by his standards but was clinical when his team needed him most from the penalty spot. 6
Riyad Mahrez's spot kick put City on level terms after Bernardo Silva was brought down
Jesus: Mis-timed an early header which seemed to unsettle him and he struggled to make an impact after that. Booed off after involvement in Gabriel red card. 5
Gundogan: (replaced Jesus 63) 4
Subs not used: Steffen, Walker, Grealish, Fernandinho, Kayky, Mbete, Palmer, McAtee.
Ref: Stuart Attwell: let the game flow, but lost control over City's controversial penalty decision and never got it back. 4
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