Chelsea saw Willian and Ramires sent off, and manager Jose Mourinho sent to the stands, in a wild end to a match settled by Fabian Delph's impudent 82nd-minute goal at Villa Park.
City leapfrogged Arsenal and Liverpool into second place by overcoming the 10th-minute sending-off of captain Vincent Kompany to win at Hull thanks to goals by David Silva and Edin Dzeko.
City has three games in hand over Chelsea, while Liverpool and Arsenal are seven points back having played two fewer matches.
The battle to avoid relegation also heated up, with the bottom seven teams separated by just five points after last-place Fulham beat Newcastle 1-0 for the team's first victory under new manager Felix Magath.
Cardiff conceded a goal three minutes into injury time to lose 2-1 at Everton and is now just a point above Fulham along with Sunderland, which drew 0-0 with Crystal Palace.
West Bromwich Albion won 2-1 at Swansea to move three points clear of danger, Norwich remained in trouble by losing 4-2 at Southampton and Stoke beat West Ham 3-1 in a match between two mid-table teams.
Chelsea looked to be marching to the title in Mourinho's first season back at Stamford Bridge, but a first defeat in 15 league matches offers plenty of encouragement to its title rivals. Arsenal and Liverpool will look to take full advantage on Sunday when they play Tottenham and Manchester United, respectively.
Willian had already been sent off for two bookings, the second coming in the 68th for a slight tug of an opponent's jersey, when Delph ran onto Marc Albrighton's cut-back and flicked a left-footed finish from behind his right foot and into the corner.
Ramires was then dismissed for a lunging tackle on Karim El Ahmadi that was described by Villa manager Paul Lambert as a "leg-breaker." In the ensuing melee, Mourinho was ordered from the dugout by referee Chris Foy.
"I asked for five seconds to ask one single question," Mourinho said. "I had no question because I was sent to the stands."
Doubts were suddenly swirling around Man City's title bid after a slump in form that saw the team lose to second-tier Wigan in the FA Cup quarterfinals, eliminated from the Champions League by Barcelona, and slip nine points off the pace in the Premier League.
A win in adversity at Hull will silence the doubters, especially considering Kompany's early red card for pulling back Nikica Jelavic when last man.
"Playing with one player less for 80 minutes is very difficult," City manager Manuel Pellegrini said. "It was a great performance. We played well with and without the ball."
Silva curled home the opening goal from outside the area in the 14th minute and the Spain playmaker set up Dzeko for the clinching second in the 90th.
Everton climbed into sixth place above Man United, boosting hopes of securing European football for next season, with a win over Cardiff at Goodison Park that was secured when Seamus Coleman mis-hit a shot into the net with seconds remaining in stoppage time.
Gerard Deulofeu, on loan from Barcelona, made the home team's breakthrough in the 59th following a string of brilliant saves by Cardiff goalkeeper David Marshall. Juan Cala bundled in a scrappy equaliser for next-to-last Cardiff in the 69th.
The heart-breaking defeat was made all the worse for Cardiff with the news of Fulham's victory over Newcastle, courtesy of Ashkan Dejagah's goal in the 68th.
Fulham is just three points away from safety after its first win since New Year's Day.
Stephane Sessegnon and Youssouf Mulumbu scored second-half goals as West Brom came from behind at Swansea to give under-pressure manager Pepe Mel his first win since taking over on Jan. 9.
"We know we are a good team even if every newspaper you read says we are going to go down," said Mulumbu, who grabbed an 85th-minute winner. "I think in the second half we showed the real face of West Brom and I hope we are going to keep doing that."
Morgan Schneiderlin, Rickie Lambert, Jay Rodriguez and Sam Gallagher were the goalscorers for Southampton against Norwich, which is four points off the bottom three but has played more games than most of its relegation rivals.Suggest a correction