Having been knocked down into second place by Manchester United's win over Crystal Palace earlier in the day, Pep Guardiola's side jumped back ahead of their city rivals on goal difference thanks to Kevin De Bruyne's superb second-half strike.
City are now unbeaten in 15 league games and have dropped only two points this season. Chelsea sustained their second defeat of the campaign at Stamford Bridge and fall to fourth, six points adrift of the two Manchester clubs and one behind Tottenham Hotspur, who are third.
Their poor performance and result were compounded by losing top scorer Alvaro Morata to injury in the first half when he limped off, holding his hamstring.
"It ends a very nice month for us," De Bruyne told BT Sport. "It's only the beginning but it's good to maintain the winning streak. We want to win as many as possible.
"We played tactically a great game, It's a nice win because it's difficult to win here. We want to lose as less game as possible because the feeling when you win is better.
"We have two games with the national team and then come back and continue."
Meanwhile, Manchester United maintained their impressive form in the English Premier League as they secured a four nil win over Crystal Palace. Juan Mata opened the scoring for United before Marouanne Fellaine added the second goal minutes later.
Fellaini added the third goal after the break with Romelu Lukaku scoring the fourth goal as United remained unbeaten in the league so far. Elsewhere, Harry Kane struck twice as Tottenham beat Huddersfield four nil in an earlier kick off.
-The Star