Saido Berahino’s maiden Premier League goal gave brilliant Albion their first win at Old Trafford for 35 years.
Morgan Amalfitano scored a magnificent goal on 54 minutes to put the Baggies ahead, only for Wayne Rooney’s free-kick to creep in for the equaliser just three minutes later.
But 20-year-old Berahino finished superbly after a fine Albion move on 67 minutes to secure an historic triumph for Steve Clarke’s men.
And watching from the press box was Baggies legend Tony Brown, who made his debut 50 years ago today and scored twice in the club’s last win at Old Trafford – the legendary 5-3 victory in 1978.
Albion suffered an early blow when they lost the services of Scott Sinclair after 13 minutes.
The loanee won a race with Nani but then went down holding his hamstring and was replaced by Saido Berahino.
And United made the early running with Nani looking dangerous.
First he had a cross claimed low down by Boaz Myhill after Javier Hernandez just failed to make contact, then he fizzed the ball across goal again with Wayne Rooney inches away from turning it in.
But Albion had their moments, too, with Victor Anichebe forcing a corner and a weaving run by Stephane Sessegnon sparking a goalmouth scramble in which United eventually cleared.
And, despite absorbing plenty of pressure, Albion should have led just before the half-hour when a corner from Morgan Amalfitano was returned to the Frenchman on the left.
He delivered a glorious cross and Berahino crept between two defenders but headed an excellent chance wide.
United hit the bar through Anderson from a Shinji Kagawa cross although the linesman had, incorrectly, already raised an offside flag.
But Albion grew in confidence and on the stroke of half-time they could have led from an Amalfitano corner that was headed on by Claudio Yacob to the far post.
But Sessegnon lashed at the shot and it flew well off target.
Early in the second half Billy Jones made a crucial tackle just inside the penalty area to deny half-time United substitute Adnan Januzaj.
But the Baggies then had another glorious chance to take the lead when a flick from Amalfitano sent Sessegnon running at the United defence.
He weaved his way to the edge of the area but opted not to shoot and teed up Berahino, whose shot was blocked by David De Gea.
Albion went ahead on 54 minutes with a moment of brilliance form Amalfitano.
He picked up possession on halfway and ran 35 yards before nutmegging Rio Ferdinand, bursting into the United area and chipping the advancing De Gea.
But the lead lasted for just three minutes before United grabbed a fortunate equaliser.
Billy Jones tripped Alexander Buttner on his way to goal and Rooney’s free-kick crept through a crowded box and into the net as Boaz Myhill waited for a touch from Hernandez.
Albion were back on dreamland on 67 minutes, however, as another brilliant goal restored their lead.
Sessegnon lifted the ball to the edge of the box, where Amalfitano’s neat lay-off set up Berahino for a brilliant finish and a first Premier League goal.
Albion had another chance when the ball fell to Sessegnon after a neat move but he dragged his shot wide.
But there was a crucial block on the Albion goalline by Jonas Olsson to keep out a right-wing cross-shot.
By Steve Madeley