Looking to get over their Europa League exit in midweek, City started well and Petr Cech had to be alert to deny Yaya Toure after the Ivorian midfielder had been played in by David Silva.
The hosts, meanwhile, grew into the game and their first opportunity of the game should have fallen to Salomon Kalou but he was tripped by a team-mate and the chance went begging.
Chelsea began to take control and it took a superb tackle from Nigel de Jong to prevent Fernando Torres from racing through on goal before Kalou’s turn and shot was well saved by Joe Hart.
Kalou’s frustrations grew after he was again denied by Hart, this time after good work from Torres and Florent Malouda, but the Blues finally broke the deadlock with 12 minutes remaining when David Luiz earned a free-kick and was then on hand to head home Dider Drogba’s set-piece.
Ramires then wrapped up the three points in added time when cut through the City defence before calmly slotting past Hart, and the win meant Chelsea leapfrogged their visitors into third place.