Paul Robinson's header deep in injury time rescued a point for West Brom to lift them out of the relegation zone.
Robinson struck at the far post to convert Riccardo Scimeca's cross.
Darius Vassell had put Villa ahead, pouncing on a rebound after Russell Hoult superbly palmed Liam Ridgewell's header on to his crossbar.
Both Hoult and Thomas Sorensen made good saves, while Ridgewell and Jonathan Greening both saw red for head-butting after the break.
West Brom, with three wins in their previous four games, are now fourth-bottom in the Premiership and playing like a team who believe they can retain their Premiership status.
But it seemed for so long as though Villa would take all the points to boost their flagging hopes of qualifying for European football next season.
Villa went into the match on a sequence of win-one, lose-one that stretched back six games.
And having defeated Newcastle 3-0 last week, David O'Leary's team started at a bristling high-tempo, clearly determined to end their inconsistent run of form.
Hoult bravely came off his line to smother Vassell's short-range strike, while Juan Pablo Angel headed wide and shot over.
Samuel almost lobbed Hoult from a tight angle, but the Baggies keeper managed to turn the ball over his crossbar.
From the subsequent corner Villa's committed start was rewarded with a goal.
Ridgewell made a superb contact from Nolberto Solano's corner and Hoult did brilliantly to parry his header against the crossbar.
Vassell was the first to pounce upon the rebound to put Villa in front.
But with half-time looming the Baggies squandered two chances to equalise.
Ridgewell and Greening were both sent-off
Ronnie Wallwork delivered a precise far-post cross from the right but Kevin Campbell made weak contact and his poorly directed header was easily saved.
Then Laursen made a committed block to deflect a short-range shot from Campbell over after Richardson's deft flick had created the opening.
West Brom created another good chance shortly after the restart, Martin Albrechtsen's cross eluded Thomas Sorensen and Laursen bailed out his keeper, clearing at the second attempt with Geoff Horsfield lurking.
Tensions rose when Ridgewell and Jonathan Greening clashed, locking heads and attempting to head-butt each other several times without seeming to make any meaningful contact.
Both saw red for their foolish behaviour and the match swung back in Villa's favour, with Hoult brilliantly saving a Vassell header.
But the Baggies refused to give up and Sorensen did well to save from Gera.
And West Brom's tenaciousness was rewarded when Delaney inadvertently flicked Riccardo Scimeca's cross to the far post - with Robinson pouncing to score his first goal for the club.
Aston Villa manager David O'Leary:
"I thought we should have wrapped it up in the first half and even though we were a shadow of ourselves in the second half, we should still have won the game.
"It sums up our season. We have made too many silly mistakes and got one point instead of three.
"We wanted to build on a great performance at Newcastle last week but we haven't done that."
West Brom manager Bryan Robson:
"It is only a point but it is the manner in which we got it which keeps the momentum going.
"The lads are in good form and really believe in themselves at the moment. It was important we got something out of the game.
"I was really pleased with the response in the second half. We competed really well, created some good situations and deserved a point."
Aston Villa: Sorensen, Delaney, Laursen, Ridgewell, Samuel, Solano (De la Cruz 64), Hendrie, Davis, Barry, Angel (Cole 80), Vassell.
Subs Not Used: Hitzlsperger, Postma, Berson.
Sent Off: Ridgewell (61).
Goals: Vassell 27.
West Brom: Hoult, Albrechtsen (Scimeca 80), Gaardsoe, Clement, Robinson, Gera, Wallwork, Richardson, Greening, Horsfield (Earnshaw 71), Campbell (Kanu 71).
Subs Not Used: Moore, Kuszczak.
Sent Off: Greening (61).
Booked: Robinson, Kanu.
Goals: Robinson 90.
Ref: R Styles (Hampshire).