The French midfielder linked up with the returning Carlos Tevez five minutes from time to earn City a 20th consecutive home league victory and lift them to within a point of leaders Manchester United.
Chelsea took the lead through Gary Cahill's deflected shot on the hour but Sergio Aguero levelled from the penalty spot.
Third-placed Tottenham Hotspur drew 1-1 at home with Stoke City in their first game since their FA Cup tie against Bolton Wanderers was abandoned following Fabrice Muamba's cardiac arrest.
Arsenal could move above Tottenham into third place with victory over Everton in a later kickoff while Chelsea remain outside the top four in fifth place, four points behind Tottenham who they host this weekend.
Liverpool were also in action against Queen Park Rangers in another match that kicked off later.
(Reporting by Martyn Herman, editing by Ed Osmond)
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