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.
Chelsea have taken just 10 points from the last 30, a run that leaves them in fifth place on 35 points, one behind Tottenham Hotspur and four behind Arsenal. Manchester United and Manchester City lead the way with 41 points.
"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."
Chelsea had gone ahead with a Frank Lampard penalty after 23 minutes but Villa restored parity with their own penalty, by Ashley Young, just before halftime.
An Emile Heskey header put the visitors ahead early in the second half and after Brad Friedel made three great saves it looked as if Villa would hold on for a morale-boosting win.
The American keeper did well again to block a Salomon Kalou shot after 84 minutes but Drogba forced the rebound through three defenders to make it 2-2.
Terry then seized on another rebound to shoot home what he and most of the stadium greeted as the winner in the 89th minute.
However, Chelsea inexplicably allowed Clark to ghost in unmarked at the far post to nod in Marc Albrighton's cross.
HOULLIER DEFIANT
Villa, who have now taken four points from a possible 21, started the day a point above the relegation zone and ended it in 15th place, two points above the bottom three.
Yet their manager, Gerard Houllier, said reports of unrest within his squad were false.
"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.
Friedel, the man of the match, said Villa had showed grit.
"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
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