Aidan White scores Leeds' first goal during the Capital One Cup Third Round match against and Everton.
Villa beat City 4-2 after twice coming from behind to force the game into extra time, when Charles N'Zogbia and Gabriel Agbonlahor scored.
Goals from Aidy White and Rodolph Austin put Leeds into the fourth round with a 2-1 victory over Everton, which is third in the Premier League.
But it was completely one-sided at Chelsea, with Fernando Torres among six different scorers as the Premier League leaders crushed Wolves 6-0.
Man City's patchy form in the league, however, extended into the first domestic cup competition of the season.
Despite manager Roberto Mancini making 10 changes from Sunday's 1-1 draw with Arsenal, the team's combined value was still more than $200-million.
Mario Balotelli gave a strong City side the lead in the 27th minute, but the visitors drew level thanks to an own goal by former Villa midfielder Gareth Barry in the second half.
Equalised
Aleksandar Kolarov restored City's lead before Villa equalised again when Agbonlahor scored his first of the night in the 70th.
N'Zogbia scored six minutes into the first extra period with a low shot from close range, and Agbonlahor sealed victory with a fine strike near the end.
"It was a difficult match because Aston Villa were a good team," Mancini said. "We didn't play well and we had some unlucky moments, but I think they deserved to go through."
Mancini exchanged heated words in the second half with Villa manager Paul Lambert after complaining to the fourth official about a tackle on Barry by Joe Bennett.
"It is a massive result for us. I thought the way we played was excellent," Lambert said.
At Elland Road, Leeds stormed in front after four minutes when Aidan White weaved his way through the visiting defence before unleashing a fierce drive into the net.
Doubled lead
Leeds doubled its lead with 20 minutes remaining when Danny Pugh's shot was backheeled into the net by Rodolph Austin, ensuring Sylvain Distin's late header was only a consolation.
"We started terribly, gave them the initiative and lost the game in the opening 20 minutes due to the way we started," Everton manager David Moyes said. "We gave away a really poor first goal and left ourselves trying to get back into the game."
At Stamford Bridge, Chelsea captain John Terry played after appearing in front of a Football Association racism hearing for a second day.
Gary Cahill, Ryan Bertrand and Juan Mata all scored inside the opening 17 minutes against a heavily weakened Wolves side, while Oriol Romeu netted from the penalty spot earlier in the second half before Torres and Victor Moses added further goals.
Also Tuesday, Swansea was spared from embarrassment late on at Crawley, coming from behind and scoring in stoppage time to beat the third-tier side 3-2.
Wigan eliminated West Ham with a 4-1 victory, Southampton defeated Sheffield on Wednesday 2-0, and Sunderland won 2-0 at MK Dons. – Sapa-AP