It had briefly looked like both the top two may drop points when Villa ended a near 11-hour goal-drought to level the scores at Villa Park, but a thunderous finish from Branislav Ivanovic maximised the embarrassment for their main title rivals.
"Apart from the first 15 minutes of the second half we had good control of the game and we showed good ambition after it went to 1-1," Chelsea boss Jose Mourinho told reporters.
"Our second goal showed that. The left back was in the box to cross and the right back was in the box to finish. We pushed hard. It was a very important victory."
City needed a stoppage-time free kick from James Milner to rescue a point against relegation-threatened Hull, but it still left them winless since the start of the month when midfielder Yaya Toure packed his bags for the African Nations Cup.
Prolific Tottenham Hotspur striker Harry Kane marked his first north London derby against Arsenal with a double strike that hauled his side back from a goal down to win 2-1, moving them above their neighbours into fifth place in the table.
Southampton scored deep into stoppage time to beat Queens Park Rangers 1-0, moving them back into third place in an increasingly congested scrap for a top-four finish and Champions League qualification.
Liverpool drew 0-0 at Everton in a dour derby, Steven Gerrard's last for the Reds, which did little to help his seventh-placed side nudge up towards the Champions League spots.
Everton remained 12 points behind their city rivals in 12th.
Crystal Palace's resurgence under Alan Pardew continued with a 1-0 win at Leicester City which moved them up to 13th and left their opponents bottom. Swansea City and Sunderland drew 1-1.
(Editing by Ed Osmond/Mark Meadows)
