Olsson's deflection the winner
Man United stay in fourth
United lose three matches in a row
Baggies seven points clear of drop zone
So Manchester United start in fourth, but will go back above Arsenal and rivals Manchester City with a win, with City playing Tottenham on Sunday and Arsenal facing Hull on Monday.
Liverpool remain in contention for a top-four finish, but have played at least a game more than United, City and Arsenal.
So this is the bottom of the Premier League table. Are West Brom safe? Well, after wins for Sunderland and Leicester, maybe not just yet. Tony Pulis's side have four games left, but after Manchester United today, travel to Newcastle before ending the season with games against Chelsea and Arsenal.
So it has already been a busy day in the Premier League.
These are the results from the other games.
For manager, player and pundit from these games, follow our separate live text commentary for all the best quotes.
As always, we want your thoughts and comments on this match. Get involved using the hashtag #bbcfootball, leave a message on the BBC Sport Facebook page or text us on 81111 (UK only).
So no Angel Di Maria in Manchester United's starting line-up. But boss Louis van Gaal expects the winger to remain at the club despite being disappointed by the Argentina international's first season in English football since his £59.7m move from Real Madrid.
Image source, Getty Images"He cannot say that he has had a marvellous season here," said van Gaal. "He is not always in the line-up which for him a disappointment, but also for me a disappointment.
"But he is working hard. I'm pleased with his attitude, so that's not a problem. I think Di Maria shall stay.
"The decision is not only to him because we have a contract, and we always speak with every player about the future. That is the same with every player."
Manchester United XI: De Gea, Valencia, Smalling, McNair, Blind, Mata, Herrera, Fellaini, Young, Rooney, van Persie.
West Bromwich Albion XI: Myhill, Dawson, McAuley, Olsson, Lescott, Brunt, Yacob, Gardner, Mulumbu, Fletcher, Berahino.
Image source, Getty ImagesOnly one change for Manchester United from the side that lost 3-0 at Everton on Sunday. And it is an attacking one from Louis van Gaal as Robin van Persie comes into the side, to replace Luke Shaw, who is not in United's 18. It means Angel Di Maria remains on the bench, and is joined by Phil Jones who has recovered from an ankle injury.
West Brom boss Tony Pulis changes two of his starting 11 from the 0-0 draw against Liverpool as Jonas Olsson and Youssouf Mulumbu come in for James Morrison and Victor Anichebe.
Hello, good afternoon and welcome to BBC Sport's live text commentary for the Premier League match between Manchester United and West Brom.
So, no time to waste. It is time for the team news from Old Trafford.
From beating Bayern Munich in the most amazing finish possible with two goals in injury time in 1999...
Image source, Empics... to a dramatic penalty shoot-out win against Chelsea in 2008. The Champions League has provided some of the best moments for Manchester United supporters.
Image source, Getty ImagesBut not this season. This season United's players could leave their passports locked away as they had to watch on enviously from the sidelines.
Image source, Getty ImagesBut the good times may be returning to Old Trafford. A victory today and Champions League football could well be back on the menu.
Image source, Getty Images