A first-half goal from Phil Jones was followed up with strikes from Wayne Rooney and Danny Welbeck as David Moyes' side piled the pressure on their relegation-threatened hosts.
West Brom began the game on the front foot, but United showed menace on the counter-attack.
Their much-vaunted front four of Juan Mata, Adnan Januzaj, Rooney and Robin van Persie showed more cohesion than in previous games, but it was Chris Brunt who almost put United ahead after 16 minutes.
The West Brom captain inadvertently diverted Marouane Fellaini's 16th-minute header goalwards before Youssouff Mulumbu came to his rescue by clearing off the line.
The hosts then had former United goalkeeper Ben Foster to thank for keeping them level just before the half-hour mark when he kept out Rafael's powerful back-post header.
There was nothing Foster could do about the 33rd-minute opener, however, as Jones glanced Van Persie's free-kick past the keeper from eight yards for his first Premier League goal of the season.
West Brom should have drawn level five minutes later when Claudio Yacob nodded over from three yards, before Victor Anichebe outmuscled Jones with his back to goal only to drag wide from 12 yards.
Foster appeared fortunate to escape punishment just before half-time as he seemed to handle outside his area, with referee Jonathan Moss waving play on despite vehement protests from Moyes.
Mel's side came began the second period as they started the first, and created a clear opening after 52 minutes only for Zoltan Gera to shoot tamely straight at David de Gea after a neat one-two with Anichebe.
Moss was again in the spotlight shortly after, as he deemed Van Persie's second wild lunge in the space of five minutes unworthy of a second booking.
The referee cautioned the Dutchman for his first poor tackle on Morgan Amalfitano, and could easily have dismissed him when he went in late on Steven Reid shortly after, but opted instead for a stern warning.
Moyes, perhaps mindful of his striker's fortune, substituted Van Persie for Welbeck just after the hour mark.
United were struggling to contain Anichebe's physicality, and the former Everton man almost created the equaliser when he fired across goal after once again shrugging off the attentions of Jones, but Rafael was on hand to clear before Brunt could tap in to an open goal.
Despite West Brom's promising start after the interval, they were undone by a moment of real quality from the visitors as Rooney doubled their advantage after 65 minutes.
Slick interplay between Rooney, Mata and Rafael ended with the Brazil defender finding the unmarked England striker with a pinpoint cross, and he made no mistake with a simple back-post header.
Welbeck then made sure seven minutes from time when he latched on to Rooney's perfectly weighted throughball and produced a smart finish.