United went into the game looking to close the gap on leaders Manchester City to 11 points and they came out of the blocks like a house on fire early on.
West Brom could barely get a hold of the ball in the first 10 minutes, but United were unable to make their immediate dominance count.
Despite enjoying almost all of the possession there were very few clear-cut chances created by United in the first half, but when they did create one, Romelu Lukaku made no mistake.
With 27 minutes gone, the lively Marcus Rashford shifted the ball onto his right foot and crossed into the middle. The ball was perfect for Lukaku, who rose to flick a header past Ben Foster and into the far corner to give United the lead and continue his fine personal record against his former side.
8 - Romelu Lukaku has had a hand in eight goals in eight @premierleague games against former club West Brom (five goals, three assists). Haunt. pic.twitter.com/x0Lm5fNE8r
— OptaJoe (@OptaJoe) 17 December 2017
West Brom reacted well, with Chris Smalling being forced into two excellent pieces of defending to maintain the lead.
First, he made a fine sliding challenge as Oliver Burke, making his first Premier League start, threatened to race away down the left. Before he somehow managed to prevent Salomon Rondon from bundling home at the near post after good work from Ally Nyom down the right.
Within minutes, United had gone down the other end and doubled their lead. Jesse Lingard was afforded time to drive forward and shoot and his low effort deflected off the hapless Ahmed Hegazi and past Ben Foster in the home goal.
Jake Livermore saw a tame low effort kept out by David De Gea on the stroke of half-time as United went into the break with a two-goal lead.
West Brom improved in the second period, but United continued to threaten on the counter.
Kieran Gibbs dragged an effort wide before substitute Gareth Barry fired straight at De Gea from the edge of the box.
United had two chances to extend their lead just before the hour mark as first Rashford saw an effort skid wide of the far post after excellent play from Antonio Valencia down the right, before Lingard could only fire straight at Foster after a rapid break.
As time ticked on, the hosts started to push more and more men forward.
United were doing a good job of getting bodies in the way of things but from one of the corners they conceded West Brom were handed a lifeline.
Chris Brunt whipped the ball in from the right and United failed to clear, leaving Barry with the simple task of tapping home from close range for his first goal as a substitute since 1999.
6812 - Gareth Barry has scored his first @premierleague goal as a substitute in 6812 days, with his previous one coming for Aston Villa in April 1999 (v Nottingham Forest). Eternal. pic.twitter.com/7WHbYo22ut
— OptaJoe (@OptaJoe) 17 December 2017
As is often the case, there was enought time left for one more great chance, with Brunt heavily involved once again.
The Northern Irishman found a yard of space down the left and swung in a perfect ball for Jay Rodriguez but the former Southampton man headed narrowly wide of the near post when he really should have scored.
Lukaku wasted a chance to add some gloss to the scoreline late on as he shot when he could have played in Jaun Mata.
That proved to be that for West Brom, who missed the chance to move out of the relegation zone, United meanwhile now switch their attentions to their Carabao Cup quarter-final against Bristol City on Wednesday.