Manchester United went into the clash without the injured Wayne Rooney but with a one-point advantage at the top of the table.
However, the hosts fell behind in the 20th minute when Joe Cole flicked in Florent Malouda's pull-back to put Chelsea ahead.
United improved after half-time but found themselves two down with 11 minutes left as substitute Didier Drogba slammed the ball past Edwin van der Sar, although replays showed the striker was clearly offside as he collected Salomon Kalou's pass.
United replacement Federico Macheda pulled one back within two minutes when Petr Cech pushed Nani's cross onto the chest of the youngster - this time Macheda getting the benefit of the doubt when he handled.
Dimitar Berbatov had the best chance to force a draw but his 90th-minute but his snapshot from the edge of the area was easily saved by Cech.
PREMIER LEAGUE TOP SIX
Team Pl GD Pts 1 Chelsea 33 +54 74 2 Man Utd 33 +50 72 3 Arsenal 33 +41 71 4 Man City 32 +24 59 5 Tottenham 32 +26 58 6 Liverpool 32 +21 54