Rooney took his tally to nine goals from his last six matches and 26 for the season, opening the scoring with a clever volley in the 36th minute and doubling the lead with a clinical 71st-minute penalty at Old Trafford.
The win lifted the champions to 67 points from 28 games, one more than Manchester City who are second after leading the table since the middle of October.
United manager Alex Ferguson was a happy man after his team bounced back quickly from their shock home Europa League defeat by Athletic Bilbao.
“It was a surprising day for us I suppose, but we needed that performance after the disappointment of Thursday,” he told Sky Sports News.
“We played some fantastic football today and we should have scored a lot of goals. The most important thing was the performance and hopefully the goals can come later.”
United were installed by bookmakers as the new favourites to win what would be an unprecedented 20th title and Ferguson was delighted to have hit the top.
“I am happy to be there because only a few weeks ago we were five, then seven points behind them, now we are one point ahead, so we have turned around eight points and that’s credit to the players and shows the resilience of our squad because, as everyone knows, we have had a lot of injuries,” he said.
West Brom started the brighter but United got into their stride to lead and the balance tipped their way even further when West Brom had Jonas Olsson sent off for a second bookable defence after tripping Javier Hernandez in the 66th minute.
Hernandez had gone close earlier for United, thumping a fine strike against the post.
City did not come back from their Europa League defeat at Sporting with a win and manager Roberto Mancini rued their recent lack of goals.
“For the last 10 minutes of the first half and throughout the second half we had control of the game and should have scored,” he told Sky.
“But we did not score and made a mistake at the end to concede a goal. We had the chances but we needed to score and if you don’t score, like against Sporting and now for two games, well, clearly, it’s a problem.
“We might be in a difficult moment now, but there are still 10 games to go.”
City could have fallen behind in the seventh minute when Joe Hart conceded a penalty after bringing down Wayne Routledge before redeeming himself by saving Scott Sinclair’s spot-kick.
City then had plenty of possession but could not find that elusive goal. With the game seemingly headed for a goalless draw that would have kept City top on goal difference, the deadlock was broken seven minutes from time.
Luke Moore, who had been on the field for four minutes after replacing Danny Graham, found himself unmarked in space and this time Hart was powerless to stop the effort, following Routledge’s perfect cross.
Micah Richards thought he had equalised for City in the dying minutes, but his effort was ruled offside.
Swansea, playing in the top flight this season for the first time since 1983, are effectively safe from relegation after a series of good performances throughout the campaign.
“This is our best result against one of the best squads in European football,” their manager Brendan Rodgers said.
“Our mentality in the game was outstanding, with our talent and ability to work. We were clearly the better side throughout the game. We retained our positivity and when we had to defend, we defended well.
“We’ve got 10 games to play and want to finish strong, sprinting over the line, not just get over it. Today is all about the Swansea City players and I can’t think of better days.”
In the day’s late game, Norwich City drew 1-1 at home with bottom-placed Wigan Athletic who saved a point with a well-taken 68th-minute equaliser from Victor Moses who rounded goalkeeper John Ruddy to score.
Norwich, who were promoted along with Swansea last season and also look safe in mid-table, went ahead with a Wes Hoolahan volley after 10 minutes.
The result left Wigan bottom on 21 points, one behind Wolverhampton Wanderers and Queens Park Rangers, who both lost on Saturday. — Reuters