Postpublished at 17:03 British Summer Time 9 May 2015
There's full post-match reaction in our main live text commentary, where we'll also have updates from Manchester United's visit to Crystal Palace. But that's all from me. Thanks for your company.
Aston Villa XI: Given; Bacuna, Vlaar, Okore, Richardson; Cleverley, Westwood, Delph; N'Zogbia, Grealish; Benteke.
West Ham XI: Adrian; Jenkinson, Collins, Burke, Cresswell; Noble, Kouyate; Downing, Nolan, Amalfitano; Valencia.
Mike Whalley
There's full post-match reaction in our main live text commentary, where we'll also have updates from Manchester United's visit to Crystal Palace. But that's all from me. Thanks for your company.
David Cameron, I'm sure, will be celebrating tonight.
Unless he really does support West Ham after all.
Some snap reaction from Villa's match-winner Tom Cleverley: "We've certainly given the fans value for money over the last 10 games. We don't make it easier for ourselves, but we've given ourselves a massive help in [our bid to] stay up. Our defence was magnificent today.
"I think we've shown we've got Plan A and a Plan B in recent weeks. We need to keep it going now."
Here's the bottom six. If you support Villa, it makes great reading - because your team aren't in it.
What a big win that is for Aston Villa - that has moved them four points clear of the bottom three.
Hull have lost 1-0 at home to Burnley, Newcastle have drawn 1-1 at home to West Brom, and Leicester have beaten Southampton 2-0.
West Ham win a corner. Nene floats the ball in, but James Collins' header drops wide. Is that it?
But suddenly, Villa find a way out - and it's Gabby Agbonlahor chasing on to a long pass and running clear of Aaron Cresswell.
But the Villa man cannot keep his composure, and rolls a shot wide under pressure. Still 1-0. About two minutes of stoppage time left.
West Ham enjoying most of the possession now. Tim Sherwood looks at his watch and asks the fourth official how long there is to go. The answer is four added minutes.
Carlton Cole tries to make a nuisance of himself inside the Villa penalty area, flicking on a cross into the area, but keeper Shay Given - 39 years young - sprints off his line to catch. There's more pressure to come, though...
Gabby Agbonlahor surges forward for Villa as the crowd roar him on. Villa have missed him during his time out injured. West Ham deal with the initial danger, but the ball runs loose to Ashley Westwood, who rolls a shot wide from just outside the area.
Jonathan, Peterborough: Aston Villa are playing great football under Tim Sherwood. Full credit to him. Great manager.
Inside the last 10 minutes. Nails are being bitten at Villa Park.
By the home fans, obviously. I doubt West Ham's fans are getting too tense over the whole Europa League fair play thing.
A change at the back for Villa as Tim Sherwood looks to secure victory. Alan Hutton comes on for Leandro Bacuna in a straight swap at right-back.
West Ham have brought on one-time Villa striker Carlton Cole for midfielder Mark Noble. Cole hasn't scored in the league since 18 October. How about now?
As things stand, Burnley are still down.
If Leicester City win against Southampton and Newcastle United avoid defeat by West Bromwich Albion, while Aston Villa do not lose to West Ham, it doesn't matter what the Clarets do. They will be relegated.
A blow to West Ham's Europa League fair-play bid! Alex Song commits a foul for the third time in the half, this time tripping Jack Grealish, and the referee, Lee Mason, has seen enough. Song goes into the book.
It is West Ham's first yellow card of the game, though - while Everton, rivals for a Europa League fair-play place, collected two against Sunderland. Someone, deep in a bunker at the Premier League, is no doubt working out the ramifications of all this as I type.
A big roar from the Holte End as Gabby Agbonlahor makes his return from a hamstring injury to play the final 20 minutes. The Villa forward is on for Charles N'Zogbia.
Nene is looking useful on the right for West Ham. This time he delivers a lovely cross for Enner Valencia to glance in, but the Ecuador international is flagged offside. Even after looking at a couple of replays, it's a very hard one to judge - but I think the linesman has probably got it right.
A big goal at the KC Stadium, where Danny Ings has turned in a loose ball from close range to put bottom-of-the-table Burnley in front against Hull - who are in deep trouble themselves.
Former Aston Villa midfielder Steve Froggatt on BBC London: "West Ham look a totally different proposition in the second half. That raises questions about the team selection in the first."
Yes, the introduction of Nene and Alex Song for Morgan Amalfitano and Kevin Nolan has given West Ham a livelier look.