United threw down the gauntlet to Manchester City by briefly reclaiming top spot in the table with the easiest of wins at Loftus Road.
City went back to the summit after a 1-0 win over Arsenal.
Rooney scored his 15th goal of the season in the first minute and the champions missed a succession of chances before Michael Carrick’s first top-flight goal for almost two years all but sealed the points.
United could easily have scored six against a QPR side who twice went close themselves through Heidar Helguson and also saw substitute DJ Campbell miss the easiest of volleys.
The win kept the pressure on City and although Sir Alex Ferguson’s men might have crashed out of the Champions League and Carling Cup, they have taken 19 points from 21 since losing 6-1 to their Roberto Mancini’s side, proving they will not give up their title without a fight.
Ferguson would have been choking on his cornflakes on Sunday morning were he to have read a newspaper interview in which former United captain Roy Keane escalated their recent spat.
Keane has been particularly critical of the club’s youngsters, who had another chance to prove him wrong at Loftus Road – and it took them less than a minute to strike.
Rooney nodded the ball out to Antonio Valencia down the right before bursting into the box and stooping to head home the winger’s cross.
Only a desperate block from Danny Gabbidon prevented Danny Welbeck making it 2-0 two minutes later but United’s vulnerable defence was almost exposed when Heidar Helguson’s free header floated over from Joey Barton’s corner.
The game eventually settled down before a 17th-minute flashpoint that saw Rio Ferdinand booked for hounding Howard Webb.
The defender’s ire would have increased six minutes later when Welbeck was wrongly flagged offside after racing clear and steering in what he thought was United’s second goal.
But Jonny Evans, Phil Jones and Valencia ought to have made that irrelevant in the space of three minutes just before the half-hour.
First, Evans nodded Chris Smalling’s flick-on from a corner against the crossbar.
Jones – again deployed in midfield for injury-hit United – was then sent clear by Rooney only to lose out one-on-one with Radek Cerny.
Cerny, who performed heroics in the previous weekend’s defeat at Liverpool, followed that by thwarting Valencia from point-blank range, with Evans seeing his header from the resulting corner cleared off the line by Alejandro Faurlin.
QPR almost made United pay when David De Gea saved Helguson’s low strike with his leg, while Bothroyd was close with a skidding shot from 20 yards.
That was enough to silence briefly the visiting fans, who mocked their own side’s Champions League exit with a chant of “Channel 5 is wonderful”.
QPR ended the first half on top but Rooney took just 20 seconds to test Cerny with a low drive after the restart as United continued to look more likely to score the game’s second goal.
And they did just that in the 56th minute when Barton gifted the ball to Carrick, who was allowed to carry it 30 yards by a backpedalling defence before drilling beyond Cerny from the edge of the box.
Rooney just failed to get a telling connection on a difficult goalline chance before Jones was booked for upending Bothroyd.
United were looking deadly on the break and Cerny tipped over Welbeck’s curler before the striker was withdrawn for Javier Hernandez, who made a shock recovery from injury to start on the bench.
QPR responded by throwing on DJ Campbell and Adel Taarabt for Helguson and Shaun Wright-Phillips.
The gulf in class was becoming embarrassing as Jones casually sidefooted against the post with just under a quarter of the game remaining.
The two Rangers substitutes should have combined to halve the deficit 15 minutes from time when Campbell volleyed Taraabt’s cross over the bar from six yards.
Clint Hill then came on for Bothroyd and Giggs replaced Rooney, with Ashley Young also sent on for Nani late on as United easily saw out time.