The midfielder’s second-half effort diverted in off Jonas Olsson and proved to be the winner in a game dominated by Louis van Gaal’s men, who have now lost three Premier League games in succession for the first time since 2001.
Boaz Myhill made a string of good saves, while Van Persie saw his spot kick turned away by the West Brom goalkeeper after Saido Berahino was penalised for handball.
The hosts enjoyed huge swathes of possession but struggled to break down a resilient Baggies outfit, and the result means United remain in fourth place, just four points clear of Liverpool in fifth.
The visitors set their stall out early, with Pulis’ men ensuring they had plenty of men behind the ball as United dominated possession.
Ashley Young was having plenty of joy up against Craig Dawson down the left flank, and the winger had the first effort of the game as he cut on to his right before seeing his shot fly wide via deflections off a defender and Van Persie.
West Brom knew their best chance of scoring was likely to be from a set piece, and Lescott spurned a glorious opportunity as he met a corner unmarked only to head his effort straight at David De Gea.
Van Persie, making his first start since October, looked determined to find the net and nearly opened the scoring as he drilled a low shot from 20 yards which Boaz Myhill turned away, before Young’s follow-up effort deflected over thanks to Dawson’s vital challenge.
Young and Van Persie were at the centre of things again as the winger caused more problems for the West Brom defence, racing towards the line before firing a low cross which Van Persie turned just wide of the near post.
It was a frustrating opening period for United and Van Persie in particular as they couldn’t convert their dominance of possession into a half-time lead.
And Van Gaal’s side soon settled into their passing stride in the second half, but the Baggies again set themselves up to make life difficult for the hosts, and took a surprise lead on 63 minutes after former United man Darren Fletcher was brought down just outside the area.
Brunt stepped up and fired a powerful effort which hit the back of Olsson’s leg before flying into the top corner, with David De Gea given no chance.
The hosts soon had a penalty appeal turned down as the ball appeared to hit Joleon Lescott’s arm and nothing was given, but minutes later they were awarded a spot kick as Antonio Valencia’s cross hit the outstretched hand of Berahino.
But the impressive Myhill guessed correctly, diving low to his left to turn away Van Persie’s effort, before the goalkeeper denied the Dutchman again, this time from a 20-yard free kick drilled low across goal.
Paddy McNair then spurned a glorious opportunity, heading wide from an unmarked position as he met Juan Mata’s corner at the far post.
It wasn’t looking like the hosts’ afternoon, with Van Persie becoming increasingly frustrated by the heroics of Myhill. The striker powered another effort at goal, this time a low volley from 25 yards which the Baggies shot-stopper again managed to turn away.
He then produced a fingertip save to turn over substitute Angel Di Maria’s effort in stoppage time, and the visitors managed to hold on for a big win to reach 40 points and almost certainly secure survival.
Manchester United: De Gea (6), Valencia (6), Smalling (6), McNair (6), Blind (5), Mata (6), Herrera (6), Fellaini (7), Young (7), Rooney (5), Van Persie (6).
Used subs: Di Maria (4), Falcao (5).
West Bromwich Albion: Myhill (9), Dawson (7), McAuley (7), Olsson (6), Lescott (7), Brunt (6), Yacob (8), Gardner (6), Mulumbu (6), Fletcher (7), Berahino (5).
Used subs: Wisdom (6), Baird (6), Ideye (6).
Man of the match: Boaz Myhill