Rooney's close-range strike after 41 minutes proved enough to see off an unambitious Fulham side and take the champions, who survied a strong late penalty appeal, to 73 points with eight games remaining.
City had moved top on goal difference with a 1-1 draw at Stoke City on Saturday but United responded with a ninth victory from their last 10 league matches and are now favourites to retain the title.
United manager Sir Alex Ferguson, closing in on a 13th English championship with the Old Trafford club, said his team had deserved the three points despite tiring near the end.
"I thought for an hour we played very well, the passing was quick and decisive and we made some decent opportunities but Fulham put in a very determined defensive performance," Ferguson, who agreed that Fulham could have had a late penalty, told Sky Sports.
"A bit of tiredness came into our game and we started to give the ball away and they capitalised. The disappointing thing was that we never finished them off when we should have."
United struggled for fluency in the first half as Fulham initially posed some threat with American striker Clint Dempsey forcing a fine save from keeper David de Gea.
Gradually United exerted pressure and the breakthrough came with half-time approaching as a cross into the area bounced kindly off Fulham's John Arne Riise for the alert Jonny Evans to cut the ball back for Rooney to crash the ball past keeper Mark Schwarzer.
The home side improved after the break and should have spared themselves anxious late moments.
Ryan Giggs skewed one chance wide and Antonio Valencia squandered another when he shot straight at Schwarzer after being sent clear by Giggs's pass.
Schwarzer also made superb saves to twice deny Ashley Young as United searched for the killer goal.
It did not arrive, though, and Martin Jol's mid-table Fulham applied late pressure, Fulham having a strong appeal for a late penalty waved away when Danny Murphy tumbled in the area under a clumsy challenge from Michael Carrick.
"I think everyone in the stadium expected a penalty to be honest," Jol told Sky Sports. "But you have to be brave to give a penalty away at Manchester United.
"We could have had a result and I think they looked pretty nervous at the end."
Fergsuon said United should also have had a penalty but acknowledged that they had got a little fortunate.
"Certainly Michael Carrick caught Danny Muprhy's heels when he came back," Ferguson said. "But I think we deserved [some luck] because we completely dominated the game until that last 15 minutes."
