Morgan Amalfitano opened the scoring for the visitors when he drifted past Rio Ferdinand before dinking the ball over David de Gea from close range.
United hit straight back, however, as Wayne Rooney's free kick flew into the bottom corner after eluding a mass of bodies in the area.
West Brom's winner came in the 67th minute when Saido Berahino capped off a slick move with a smart finish from the edge of the box.
Here, Sports Mole takes an in-depth look at what exactly went wrong on another disappointing day for United.
On target 6
On target 4
Was the result fair?
The stats point towards a United win if anything, but in truth a draw probably would have been the fairest result today. West Brom played well and are certainly not completely undeserving winners having created just as many chances as United, but the Red Devils probably would have thought that they did enough to earn a draw.
Manchester United's performance
More disappointment for David Moyes in the league. It was a fairly uninspiring performance and they looked short of ideas in the final third without Robin van Persie to call upon. Their goal had an element of luck about it as it was not a shot, and they rarely looked like scoring at any other point. Anderson did hit the bar which was a little unlucky for the hosts, but they will have expected to play a lot better than they did today.
West Brom's performance
They will probably play better than that this season and lose games, but the result is the all-important thing. It was by no means a bad performance from West Brom, but they didn't really need to be at their best to win this match. A result at Old Trafford is a rarity, so they should make the most of the situation as it won't come round too often. The Baggies are still improving after a relatively poor start, but there were plenty of positives to take from today's match.
Sports Mole's man of the match
Stephane Sessegnon: He may not have got himself on the scoresheet today but Sessegnon was the most creative man on the field. He gave the United defence a tough time and took full advantage of the absences of the likes of Nemanja Vidic and Patrice Evra.
This one has to go to Rio Ferdinand for his attempted tackle on Amalfitano in the build-up to the opening goal. The veteran defender got nowhere near the ball or the player, letting him coast past him and go on to score. It was really poor defending and not the type of mistake you usually see Ferdinand make.
It is always said that if you do not notice the referee, then he has had a good game, and that was the case today. It was not the hardest match Michael Oliver will ever officiate, but he dealt with what he had to do well.
Manchester United: Next up for United is a return to Champions League action as they face Shakhtar Donetsk.
West Brom: The Baggies will be looking to pick up some more unexpected points when they face Arsenal at The Hawthorns next Sunday.