Fabian Delph scored a goal that could prove decisive in the final destination of the league trophy come May as Villa grabbed a 1-0 victory over the nine-man Blues with eight minutes remaining at Villa Park.
Midfielders Willian and Ramires - and manager Jose Mourinho - were all sent off as tempers flared in Birmingham.
It was a first defeat since early December for Chelsea, who must now look over their shoulders at City given the 2012 champions are only six points behind with three games in hand.
Villa, meanwhile, move into tenth place after recording back-to-back wins.
Earlier in the day, Manuel Pellegrini's City shrugged off the tenth-minute dismissal of captain Vincent Kompany to dredge up a 2-0 win at Hull City.
David Silva struck a superb long-range opener just four minutes after Kompany was shown a straight red card for hauling down Nikica Jelavic who was through on goal.
City then sealed their return to second place when Silva sent through Edin Dzeko to make it two in the final minute.
With Magpies boss Alan Pardew watching via video link from the team hotel due to his three-match stadium ban for headbutting Hull's David Meyler, Fulham substitute Ashkan Dejagah hit the only goal of a 1-0 victory on 68 minutes.
Another manager under scrutiny of late has been West Brom's Pepe Mel, who had failed to deliver a win since taking the job in January.
Roland Lamah scored for the Swans after two minutes, only for Stephane Sessegnon to equalise in the 52nd minute. Mel then punched the air in celebration as Mulumbu bent the ball past Michael Vorm with five minutes remaining.
The victory lifts West Brom three points clear of the relegation zone after 18th-placed Cardiff lost 2-1 at the death in their meeting with UEFA Europa League-chasing Everton.
On-loan Barcelona forward Gerard Deulofeu (59) and Juan Cala (68) exchanged goals in the second half and it looked like the points would be shared until Seamus Coleman fired a winner for the Toffees three minutes into stoppage time.
Southampton managed to climb to eighth after surviving a spirited fightback from Norwich to win 4-2 at St Mary's.
Morgan Schneiderlin opened the scoring inside five minutes and second-half goals from substitute Rickie Lambert (57) and Jay Rodriguez (72) looked like putting the Saints out of sight.
However, Sam Gallagher killed off any hopes of a comeback by hitting his first Premier League goal six minutes into time added on.
Peter Odemwingie's brace inspired Stoke to come from behind and beat West Ham 3-1 at the Britannia Stadium.
It took the Hammers only five minutes to take the lead through Andy Carroll but Odemwingie levelled in the 32nd minute before adding a second goal ten minutes after Marko Arnautovic notched on 69 minutes.