It was a miserable return to West Brom for Chelsea manager Roberto Di Matteo as the European champions lost 2-1 and his former side went just a point behind them in fourth.
Ahead of Manchester United's match at Norwich, City provisionally went top after Sergio Aguero and Carlos Tevez each scored twice after David Silva's opener against Villa.
In the north London derby, Arsenal beat Tottenham 5-2 after Emmanuel Adebayor's sending off swung the game in his former team's favour.
The pressure increased on Queens Park Rangers manager Mark Hughes after his winless side lost 3-1 to Southampton to stay bottom. But Reading secured its first win, beating Everton 2-1, while Luis Suarez scored twice in Liverpool's 3-0 win over Wigan and Swansea won 2-1 at Newcastle.
Southampton remains in the drop zone but moved four points above QPR by extended the London club's winless run to 12 matches.
Rickie Lambert, Jason Puncheon scored for Southampton and after Junior Hoilett of Brampton, Ont., pulled one back, QPR defender Anton Ferdinand scored a late own goal.
Swansea won at Newcastle for the first time since 1980, with goals from Miguel Michu and Toronto's Jonathan de Guzman securing a 2-1 win. Demba Ba scored a consolation goal in stoppage time.
Champion City remains the only unbeaten team.
Roberto Mancini's side took until the 43rd minute to take the lead, with Silva tucking the ball into the net from close range after Villa failed to deal with Samir Nasri's corner.
But City was far more ruthless after the break, with Aguero netting from the spot in the 54th after Andreas Weimann handled.
City was awarded another penalty 10 minutes later when Barry Bannan handled and Tevez converted his spot kick.
Aguero was on target again, with the Argentina striker scoring from a tight angle after bursting into the penalty area.
Tevez completed the rout by grabbing his second, tapping in from close range after being picked out by Nasri. The result plunged Villa into the relegation zone.
Chelsea had been in control of the Premier League in the opening weeks but has slipped to third and is on a four-game winless run.
Shane Long put West Brom in front a day after his grandmother died and revealed an "RIP Nan" t-shirt after heading in James Morrison's cross in the 10th.
Eden Hazard levelled before halftime, heading in his fourth goal of the season, but Peter Odemwingie nodded in West Brom's winner after the break from Long's cross.
At Emirates Stadium, Adebayor put Tottenham in front after 10 minutes but was sent off eight minutes later for a high challenge on Santi Cazorla.
Per Mertesacker started Arsenal's comeback with a 24th-minute header, and Lukas Podolski and Olivier Giroud both found the net before halftime.
Cazorla swept in the fourth goal on the hour before Gareth Bale reduced the deficit for Tottenham, but Theo Walcott knocked in the fifth in stoppage time to give Arsenal a lift after its worst start to a season since during Wenger's 16-year reign.
A third successive league loss for Spurs allowed Arsenal to move above Tottenham into sixth.
Everton dropped to fifth after losing at Reading despite Steven Naismith putting the Merseyside club in front.
Adam Le Fondre headed Reading level in the second half and then netted the winner from the spot after being fouled by Seamus Coleman. The victory moved Reading up to 17th place with nine points and out of the relegation zone on goal difference.
Liverpool rose to 11th place after Suarez scored twice in nine second-half minutes and then played a part in the third which saw Jose Enrique score his first goal for Brendan Rodgers' side.