Despite not putting on a vintage showing, José Mourinho's men cut the gap to Manchester City back to 11 points thanks to goals from Romelu Lukaku and Jesse Lingard. The Red Devils opened the scoring in the 27th minute with an excellent header from the Belgian, his second goal in as many games.
Lingard then secured the win with a deflected strike despite substitute Gareth Barry bundling home with a quarter of an hour left to go.
Baggies boss Alan Pardew made one change to the team that battled to a 0-0 draw with Liverpool last time out. Summer signing Oliver Burke came into the side for his first league start of the season in place of Hal Robson-Kanu. Midfielder Gareth Barry returned to the squad with a place on the bench. Ben Foster was making his 200th appearance in a Baggies' shirt.
Meanwhile, José Mourinho made three alterations to the United side that earned a tight 1-0 victory over Bournemouth in the week. Ashley Young, Ander Herrera and Marcus Rashford started in place of Luke Shaw, Scott McTominay and Anthony Martial.
Lukaku converts against former club
In what was a slow start to the game, Foster was the first to be called into action. Following a dangerous cross from Ashley Young, defender Kieran Gibbs awkwardly dealt with the ball, forcing the goalkeper to come and collect before being fouled by Romelu Lukaku.
Jonny Evans then connected from a corner mid-way through the first period but his header only served to float over the bar. Lukaku though showed him how it was done not long after and thundered home the opener for the visitors. Marcus Rashford found space on the left-wing and curled an excellent cross into the box. The Belgian striker, who had found space between Gibbs and Evans, then headed high into the net with United's first real opening of the game.
The Baggies did however have an excellent opportunity with only ten minutes of the first period left. Allan Nyom powered past Rashford and put in an teasing low cross into the box. Salomón Rondón stretched but could not get a telling touch and the ball was eventually cleared.
Red Devils strike before the break
The second goal of the game did eventually come however, and it was another for the visitors. Jesse Lingard picked up the ball on the edge of the area and surrounded by Albion bodies, plumped for goal. The ball took a defelction off of defender Ahmed Hegazi and looped up over Foster to doubled United's advantage.
Alan Pardew attempted to stem the United tide after the break and introduced the returning Gareth Barry in place of Claudio Yacob. It was the Baggies who had the first reall opportunity of the second period. Ollie Burke made a positive run down the left-wing and attempted to find Rondón. The ball however was just behind the Venezuelan though and United cleared.
Rashford had a chance of his own as he struck an exquisite volley from Antonio Valencia's cross. The ball fizzed just wide of the far post however. Lingard then combined well with Lukaku but could only find the gloves of Foster with a low effort from just inside the area.
Barry strikes to make Baggies bounce
Pardew continued to shuffle his pack and introdcued attacking duo Jay Rodríguez and Chris Brunt in an effort to threaten United's lead. The latter then proved pivotal as Albion found a route back into the clash. Whipping in a corner won by Rondon, the North Irishman found an Baggies body. With United failing to clear, Gareth Barry poked home from only yards out to give Pardew's men hope with less than 15 minutes left to go.
Albion continued to press but were not able to find a way past United's staunch rear-guard. Lukaku could have wrapped up the three points last in the day but his low shot bobbled just wide.
Despite that, United return to Manchester with another win and are now 11 points behind Manchester City in the Premier League table. They next play Leicester City at the King Power Stadium on Saturday evening in league play.
Meanwhile, West Bromwich Albion firmly remain in the drop zone on 14 points, two from survival. They next play Stoke City at the Bet365 Stadium next weekend.