Understandbly, there was an uneasy atmosphere at Old Trafford after the Premier League champions were dumped into the Europa League in midweek.
But Nani settled the nerves in the 17th minute and Rooney extended the lead 10 minutes later as United went into the break in total control.
Wolves needed an immediate response in the second half and Steven Fletcher delivered it courtesy of a thumping 47th-minute header to cut the arrears.
The goal gave the visitors the boost they desperately needed, while Alex Ferguson was left biting his nails as his team were left clinging to the lead ? until Nani struck for a second time.
Antonio Valencia drilled the ball across the box after a postive run, Danny Welbeck miskicked and the Portuguese winger was on hand to roll the ball home after 56 minutes.
And Valencia was the creator once again as Rooney wrapped up the points with his second of the afternoon six minutes later.
United survived an early scare when Fletcher fired a good chance wide after just 20 seconds.
A Wolves goal at that point would have really caused the home fans to sweat.
As it was, with Nani leading the way, they swiftly took command when he drilled the ball beyond Wayne Hennessey and into the bottom corner.
It was Nani's first Premier League goal since September 24, a week after Rooney had last found the net in league action.
Roo opened his account for the day shortly after and United cruised to half-time without breaking sweat.
But within 90 seconds of the restart, Fletcher peeled off his marker and rose above Patrice Evra to power home Matt Jarvis' far-post cross.
For a few minutes at least, United were struggling as Jarvis tormented Chris Smalling.
But when Phil Jones set Valencia away, the South American's low cross was tucked home by Nani from close range.
The goal lifted United and Hennessey was forced to bundle Jonny Evans' header round the post and twice deny Welbeck.
In between, Valencia picked out Rooney with another right-wing cross.
Though not in the greatest position, the bounce was kind and the England striker managed to shape up and smash home a difficult chance.
With the points in the bag, Fergie handed Ezekiel Fryers his Premier League debut.
But it took some smart reactions from Rio Ferdinand to prevent United conceding once more after his clearance smacked Smalling in the face.
United should have added a fifth goal six minutes from time but Roger Johnson cleared Jones' cross as substitute Federico Macheda slid in.
Man Utd: De Gea, Smalling, Ferdinand, Evans, Evra (Fryers 67), Valencia, Carrick, Jones, Nani (Young 77), Welbeck (Macheda 74), Rooney. Subs not used: Lindegaard, Giggs, Park, Gibson. Booked: Ferdinand.
Goals: Nani 17, Rooney 27, Nani 56, Rooney 62.
Wolves: Hennessey, Zubar, Johnson, Berra, Ward, Edwards (Milijas 31), Henry, O'Hara (Hunt 70), Jarvis, Doyle, Fletcher (Ebanks-Blake 76). Subs not used: De Vries, Elokobi, Stearman, Hammill.