The England striker, who limped off after an hour in United's Champions League victory over Aalborg BK in midweek, set up Wes Brown's headed opener, before sealing the points with a sublime second-half strike.
Rooney created the game's first chance on seven minutes, swinging in a corner from the left which Nemanja Vidic just couldn't convert at the far post.
Rovers responded well with Andre Ooijer feeding the ball through to Matt Derbyshire inside the box, but Edwin van der Sar saved well low to his right and the United defence just scrambled the ball clear as Roque Santa Cruz closed in.
United were moving the ball around well in midfield and on 20 minutes Dimitar Berbatov slipped in Darren Fletcher, who fired just wide of the mark.
Ten minutes later, Berbatov's fizzed cross found Ryan Giggs at the far post, but the Welshman's crisp strike was sensationally saved by the flying Jason Brown.
But from the resulting corner, United did break the deadlock when Rooney's deep cross was headed home by Brown, although Vidic appeared to impede Brown in the process.
Rovers' stand-in keeper was incensed by the lack of a whistle, but he was forced to get on with it - and that he did, denying Rooney in a one-on-one just minutes later.
As the second half got underway, Santa Cruz stung the gloves of van der Sar less than a minute in and that proved to be the Paraguay striker's last involvement as he limped off to be replaced by Jason Roberts moments later.
Rovers never really looked like they were going to score from then on but the visitors certainly did.
Cristiano Ronaldo dragged a shot wide just before the hour-mark, but set up United's second just four minutes later.
After skipping past Martin Olsson down the right, he pulled the ball back to Rooney, who curled a delightful effort into the top corner of the net.
Rooney almost netted his second shortly after when he controlled Carlos Tevez's pinpoint pass on his chest, but he lifted the ball over both keeper and bar.
Brown then twice came to Rovers' rescue, denying Berbatov with his legs and Anderson's speculative strike.
Tevez struck the post late on as Sir Alex Ferguson took the honours over protégé Paul Ince.