The England midfielder came off the bench to smash home an unstoppable spot kick in the 82nd minute after City defender Joleon Lescott blocked a shot by Daniel Sturridge with his hand.
The visitors were at that stage down to 10 men following the 58th-minute sending-off of left back Gael Clichy for two yellow cards and couldn’t recover, leaving them two points clear of Manchester United at the top of standings.
City had taken the lead through Mario Balotelli in the second minute before Raul Meireles equalized in the 34th.
The victory lifted Chelsea to third.
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