On a pivotal day in this season's title race, United go one point clear at the summit following Manchester City's 1-0 defeat at Swansea City in a match which kicked off as the same time as United's game.
Wayne Rooney opened the scoring 10 minutes from the end of a first half United dominated, and then added a second from the penalty spot with 20 minutes remaining.
The Baggies had to play the final quarter of the match with 10 men after Jonas Olsson was sent off for two bookable offences, but even with they never looked like repeating their feat in the corresponding fixture last season, when they came back from 2-0 down to claim a 2-2 draw.
United now have a slender lead to protect with 10 games of the campaign remaining. The end of West Brom's three-game winning streak sees them drop one place to 13th in the standings.
United started with Rooney, Javier Hernandez and Danny Welbeck all in attack, but perhaps the most noteworthy inclusion in the matchday squad was that of Paul Pogba on the bench at the end of a week in which there were reports the young midfielder is on his way to Juventus in the summer.
The champions were given an early scare when Liam Ridgewell's cross was met by Keith Andrews, but the Ireland midfielder could only guide his effort wide of the near post.
After that United took full control, with Paul Scholes once again orchestrating proceedings. Welbeck was also influential in his role as target man, teeing up Ashley Young for a near-post shot which was beaten away by Ben Foster before himself heading over from a corner.
David de Gea continued his good form in the United goal as he tipped Andrews's low drilled free-kick around the foot of the post.
Rooney pulled away from his marker to meet Young's cross to the far post, but could only guide the ball tamely at Foster who caught it gratefully.
Soon enough, Rooney did score to claim his 25th goal of the season. Hernandez cut in from the right and fired in a left-footed shot. As Foster set himself to dive and parry the strike, Rooney timed his run well to beat the offside trap and guide the ball past the former United keeper.
The home side resumed the match after the break in similar fashion, with Hernandez crashing a solid strike off the post shortly before Rooney's agile header was aimed right at Foster.
On the hour mark Welbeck should have doubled United's advantage when Scholes's chipped ball forward resulted in Gabriel Tamas and Olsson on the floor, but somehow the England striker contrived to strike wide of the far post with the goal gaping.
West Brom were firmly under the cosh, and their task got harder on 66 minutes when Olsson's foul on Hernandez earned him a second yellow card and a red.
Soon enough, United had their second goal after Andrews clumsily and needlessly bundled young over in the box. Rooney clinically drilled into the far corner from 12 yards to register his ninth goal in his last six games, and his fifth in his last five appearances against West Brom.
Pogba replaced Scholes for the final 20 minutes, and was given a warm reception from the home crowd despite his contract wrangle with the club, and there was more good news from the bench as Tom Cleverley made his first league appearance since October.
West Brom brought on Shane Long, who forced a good near-post save from De Gea soon after replacing Marc-Antoine Fortune, but United easily held on for their 10th win in 12 Premier League matches against West Brom.