Rooney took his tally to nine goals from his last six matches and 26 for the season, opening the scoring with a clever six-meter volley after a darting run in the 36th minute, and he made it 2-0 when he converted a 71st-minute penalty after Keith Andrews hauled down Ashley Young.
The win lifted the champions on to 67 points from 28 games, one more than Manchester City who are second after leading the table since the middle of October.
Both teams were in action on Sunday after playing in the Europa League on Thursday when they lost the first legs of their round-of-16 matches with United beaten 3-2 at home by Athletic Bilbao and City losing 1-0 at Sporting in Lisbon.
United manager Alex Ferguson was by far the happier man after his team bounced back immediately from that European setback, and City lost.
“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.”
The victory leaves United installed by bookmakers as the new favorites to win what would be an unprecedented 20th title, and Ferguson was delighted they had overtaken City at the top.
“I am happy to be there because only a few weeks ago we were 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 we have had a lot of injuries.”
West Brom started the brighter, but United got into their stride to lead and the balance tipped their way even more when West Brom had Jonas Olsson sent off for a second bookable defense after tripping Javier Hernandez in the 66th minute.
Hernandez had gone close earlier for United, thumping a fine strike against the post.
Unlike United, City did not come back from Thursday’s disappointment with a win and manager Roberto Mancini rued their lack of goals in their last two matches.
“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 with a better goal difference than United’s, the deadlock was broken seven minutes from time and it was Swansea who broke it.
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 equalized for City in the dying minutes, but his effort was ruled offside.
Moore told Sky Sports News: “That was a massive win for us and our pressure paid off today. I don’t score too many headers, but I’ll take anything and it was a great cross from Wayne.”
Norwich City were playing bottom-placed Wigan Athletic in the day’s late match (1600 GMT).
