The leaders, beaten at home for the first time in all competitions since November 2008, finished with nine men after having Juliano Belletti and Michael Ballack sent off late in the second half.
City climbed from fifth to fourth place after two goals from Carlos Tevez, one from the penalty spot, and two from Craig Bellamy after Frank Lampard opened the scoring for Chelsea.
Lampard scored a second for Chelsea from a penalty as the match moved into stoppage time.
All eyes on Terry-Bridge
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Chelsea are top with 61 points from 28 matches, one point more than Manchester United, who are without a league game this weekend as they play Aston Villa in the League Cup final at Wembley Stadium on Sunday.
The pre-match build-up was dominated by the first meeting between former Chelsea team mates John Terry and City's Wayne Bridge, since they became the focus of media attention following allegations that Terry had an extra-marital affair with Bridge's former girlfriend.
Bridge refused to shake Terry's hand in the customary pre-match greeting ritual between the two teams, but had a hand in creating Tevez's first goal and ended the afternoon by far the happier of the two men.
Four other matches were being played on Saturday including third-placed Arsenal's visit to Stoke City.
