David Luiz scored a close-range header with just 12 minutes remaining before Ramires doubled Chelsea's lead with a delightful finish in injury time.
Heads, you win: Luiz celebrates after opening the scoring at Stamford Bridge
The result sees Chelsea leapfrog City and move to within nine points ofleaders Manchester United, who have played one game more.
City, who were without influential captain Carlos Tevez, now look resigned to fighting for fourth place and the final Champions League qualifying spot.
More to follow.
Bad day at the office: Record signing Torres was substituted after failing to get on the scoresheet at his seventh attempt
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