Rooney and Nani doubles defeat Wolves
Having gone out of the Champions League following a meek defeat at Basel on Wednesday, United used Nani's first club goals in 14 games and Rooney's first in nine league games to restore some pride.
A superb volley by red-hot Robin van Persie gave Arsenal a 1-0 home win over Everton, while Liverpool beat Queens Park Rangers by the same score at Anfield courtesy of a Luis Suarez goal.
Early season pacesetters Newcastle United lost 4-2 at Norwich City, while Aston Villa won 2-1 at Bolton Wanderers, Swansea City beat Fulham 2-0 and Wigan Athletic climbed off the bottom with a 2-1 success at West Bromwich Albion.
From the opening exchanges at Old Trafford United looked determined to shake off the baggage of their European reverse and the previous week's League Cup exit, and Wolves could do little to stop them.
Nani cut in from the left to fire in the opener after 17 minutes and Rooney advanced into the box before delivering a similarly emphatic finish 10 minutes later.
Wolves, who shocked United with a 2-1 win at Molineux in February, briefly got back into it with a Steven Fletcher header two minutes after the restart, but United roared back as Antonio Valencia set up Nani and Rooney for their second goals after 56 and 62 minutes.
It was the first time United had scored more than one goal in a league game in eight attempts since they beat Norwich City 2-0 on October 1.
"I was pleased with the attacking part, which was very, very good, though we also had to defend well as they kept crossing the ball into our box," United manager Sir Alex Ferguson told Sky Sports News.
"All these 1-0s we could have scored more, but getting the second goal today relaxed us.
"The players have a great desire and really worked hard and played some good football."
Newcastle's flying start to the season is starting to seem a distant memory for their fans after they were well beaten at Norwich having picked up only one point in their preceding three games - albeit against Chelsea, Manchester United and Manchester City.
Two goals for the prolific Grant Holt and one each for Wesley Hoolahan and Steve Morison had Norwich celebrating, while Newcastle replied with two by Demba Ba either side of a red card for Dan Gosling after 65 minutes.
Arsenal had most of the ball against Everton without creating much danger but they broke through in spectacular fashion after 70 minutes, when Alex Song floated a long ball to the far post, where Van Persie crashed in a volley for his 19th goal of the season.
At Anfield Liverpool missed several chances and were kept at bay by QPR keeper Radek Cerny before Suarez headed the winner two minutes into the second half from a cross by Charlie Adam.
It ended a run of four successive home draws for Kenny Dalglish's side.