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"
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.
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.
"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
