Rooney pushes United back to first place
Rooney moved to 20 league goals this season after touching in a shot by Javier Hernandez in the 35th minute and smashing home a 71st-minute penalty to seal the points.
Hernandez also hit the post and Danny Welbeck spurned an open goal in the second half as United registered a fourth straight league win to move a point clear.
West Brom midfielder Keith Andrews had two early chances, but Jonas Olsson was sent off after receiving a second yellow card in the 66th as the visitors struggled to cope with United's attacking pressure after the break.
United manager Alex Ferguson made four changes to the side beaten 3-2 by Athletic Bilbao in the Europa League on Thursday. Rio Ferdinand returned to marshal the defense, while Paul Scholes and Michael Carrick started in midfield and Welbeck joined the attack.
West Brom had won its previous three league matches but manager Roy Hodgson was forced into two changes from the team that won 1-0 against Chelsea last time out, with captain Chris Brunt and Gabriel Tamas both starting.
The visitors started brightly, with the first clear chance falling to Keith Andrews who stabbed wide at the near post in the fifth minute from Liam Ridgewell's low cross.
United responded five minutes later when Ashley Young's shot was beaten away by West Brom goalkeeper Ben Foster after good work by Welbeck, while United 'keeper David De Gea had to tip Andrews' low free kick round the post in the 17th.
Welbeck was orchestrating most of United's best early moves, heading a corner over in the 26th before producing a backheel that almost created a goal for Young a minute later.
United's dominance grew as the half progressed and Rooney scored the opener after touching Hernandez' shot past Foster in the 35th to continue his rich scoring form.
The defending champion stepped up the pressure in the second half, with Hernandez hitting the post from the edge of the box in the 53rd.
Welbeck should have increased the advantage when Scholes' precise pass left him with a clear chance in the 59th, but his shot from an angle rolled wide with Foster stranded.
Olsson was sent off in the 66th after he scythed down Hernandez from behind to earn his second yellow card.
Soon after, Andrews fouled Young in the box and Rooney fired his second from the spot to give United a cushion and register his 26th goal in all competitions this season.
With United cruising to victory, the home fans erupted into chanting and cheers as news of Swansea City's late goal against Manchester City filtered into the stadium.