Phil Jones headed home a Robin van Persie free kick in the first half, Wayne Rooney finished a sweeping passing move with another header after the break and Danny Welbeck added a third to secure the points against a woeful West Brom side.
United, whose difficult season was compounded by a demoralising Champions League defeat to Olympiakos in their last outing, moved up to sixth in the table with 48 points while West Brom stay one place above the relegation zone.
Leaders Chelsea host Tottenham Hotspur in the big game of the day later on Saturday while at the other end of the table Cardiff City welcome Fulham and Crystal Palace are at home to Southampton.
The Baggies entered the match aiming to claim a rare double over Manchester United after a 2-1 triumph at Old Trafford in September, but the trend since then has been one of declining fortunes for the Midlanders.
The subsequent 22 Premier League matches have yielded only two victories.