Trailing 2-1 with six minutes to go, Chelsea levelled through Didier Drogba and sent their fans wild when defender John Terry made it 3-2 one minute from time with his first league goal for a year.
Yet barely before the supporters had retaken their seats, Carlo Ancelotti's champions had thrown it away when their defence went to sleep, allowing Ciaran Clark a free header from point-blank range to salvage a point for Villa.
In Sunday's other Premier League game, Newcastle United deservedly won 1-0 at Wigan Athletic thanks to a first-half goal from Shola Ameobi.
"I'm disappointed, obviously, because I think we used a lot of energy in second half to try to come back to win with a good spirit," Ancelotti told reporters.
"We did a fantastic job. We came back and scored to make it 3-2 and everyone thought the game was finished. We needed to be focused, we needed to play another five minutes.
"But we were not able to maintain concentration so it's our fault."
However, Chelsea inexplicably allowed Clark to ghost in unmarked at the far post to nod in Marc Albrighton's cross.
"I've read so many things that really stun me, that are nothing to do with the truth," he said. "Sometimes a player who is not playing calls his agent and his agent calls the press.
"You can't make a game like that and get a result and particularly react like that if you don't have some togetherness.
"I would have been very disappointed not to have got something out of the game," the Frenchman added.
"We've had many chats but there is a time when the talking has to stop, and I thought the boys showed determination. There was a different f
