Rooney's close-range strike after 41 minutes proved enough to see off an unambitious Fulham side and take the champions to 73 points with eight games remaining.
City 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 firm favourites to retain the title.
United struggled for fluency in the first half as Fulham initially posed some threat with Clint Dempsey forcing one fine save from home keeper David de Gea.
The breakthrough came with halftime approaching as Fulham failed to deal with a cross into the area and when the ball broke kindly for Jonny Evans his calm pull back to Rooney allowed the England striker to crash the ball past visiting keeper Mark Schwarzer.
United should have spared themselves anxious late moments in the second half but Ryan Giggs and Antonio Valencia squandered chances and Schwarzer made superb saves to twice deny Ashley Young.
Martin Jol's mid-table Fulham applied some late pressure and there were anxious faces in the home crowd as they had strong appeals for a late penalty waved away.
