Wayne Rooney netted a goal in each half to help United claim its fourth straight win, while West Brom's chances were hampered by a second-half red card to defender Jonas Olsson.
The Baggies produced a pair of early chances but fell behind 10 minutes before the break when Rooney cut in front of goalkeeper Ben Foster to redirect a shot from Javier Hernandez past the former United 'keeper.
Danny Welbeck missed a great opportunity to double the lead for the home side, but Olsson picked up a second yellow card for a challenge on Hernandez and Rooney punished West Brom from the spot a few minutes later to kill off the match.
Ashley Young was brought down inside the area by Keith Andrews and Rooney sent Foster the wrong way to wrap up three points.
Swansea City 1, Manchester City 0
Swansea, Wales - Manchester City fell from the top of the league table on Sunday as Luke Moore's 83rd-minute goal proved decisive in a 1-0 win for Swansea City at the Liberty Stadium.
The home side could have gone in front in the opening 10 minutes when City goalkeeper Joe Hart brought down Swansea's Wayne Routledge inside the penalty area.
But Hart redeemed himself by stopping Scott Sinclair's spot kick, although City was having a tough time breaking down the Swansea defense.
Clear-cut chances were at a premium for both sides, but it was a poor pass from City's Stefan Savic that led to the lone tally as Routledge pounced on the ball and crossed to the front of goal for Moore to head home.
Micah Richards had the ball in the net for City late on, only to have it ruled out for offsides, snapping a four-game winning streak for the Citizens and leaving the club one point back of United.
Norwich City 1, Wigan 1
Norwich, England - Wigan battled back to claim a point at Carrow Road on Sunday with Victor Moses scoring in the 67th minute for the Latics to help the team claim a 1-1 draw with Norwich City.
Wigan fell behind after 10 minutes to a Wes Hoolahan goal after he finished off Simeon Jackson's cross. But the Canaries were denied a third win in five games when Moses latched on to Shaun Maloney's through ball and beat goalkeeper John Ruddy.
The Latics saw their winless streak reach 13 games with the result, but the club is only two points from safety despite remaining on the bottom of the table.