City striker Emmanuel Adebayor cancelled out his early own goal with an equaliser before the break and, after Carlos Tevez had put the home side ahead with a 56th-minute free kick, Shay Given saved a Frank Lampard penalty.
Chelsea's third defeat of the season leaves them on 36 points, two ahead of Manchester United, who won 4-0 at West Ham United with a defence depleted through injury.
"I thought we were magnificent from start to finish," City manager Mark Hughes told ESPN.
"We got off to the worst possible start, very unlucky with the goal, but from that point onwards we took the fight to Chelsea.
"Not many teams can come back against Chelsea. To show the character and quality that we did was a fantastic effort by everybody"
Arsenal moved up to third on 28 with a 2-0 home win over Stoke City while Tottenham Hotspur, who visit Everton on Sunday, and Aston Villa, 3-0 home winners over Hull City, have 26.
Manchester City are sixth on 25, a point ahead of Liverpool after their dour goalless draw at Blackburn Rovers.
The big-money battle at Eastlands drew a record 47,348 crowd and did not disappoint, particularly in an open and entertaining first half.
OWN GOAL
Chelsea went ahead following an eighth-minute corner when Given made an excellent double save from Branislav Ivanovic and Nicolas Anelka only for the ball to bounce off Adebayor's back into his own net.
City levelled when Togo striker Adebayor seized on the rebound after a Shaun Wright-Phillips effort was blocked eight minutes before halftime.
Chelsea had won their last five league games without conceding a goal while scoring 17 but they shipped a second against City 11 minutes after the restart when Tevez curled a free kick through a ragged wall.
Chelsea poured everything forward but missed the perfect chance to equalise when Given dived to save Lampard's penalty after Drogba had been caught by Nedum Onuoha.
Manchester United took a while to establish their dominance over a West Ham side who have given them problems in the past.
However, once Paul Scholes put them ahead at the end of the first half with his first league goal of the season they were in total control despite their defensive injury crisis.
Darron Gibson thumped in a long-range second after an hour before two quick goals 10 minutes later by Antonio Valencia and Wayne Rooney completed the victory.
"Once we got that second goal we never stopped, we went to try and kill the game off," said manager Alex Ferguson, who added that injuries to Gary Neville and Wes Brown had left him down to the "bare bones".
At the Emirates, Arsenal's Cesc Fabregas had an early penalty saved by the impressive Thomas Sorensen and a goal-bound effort blocked on the line by team mate Emmanuel Eboue before Andrei Arshavin scored after 26 minutes.
Aaron Ramsey got the second in the 79th as Arsene Wenger's team, muscled
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