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The home side had a chance to level but, as Dimitar Berbatov prepared to shoot, Rafael saved his team with a last-ditch tackle.
However, Man Utd raced up the other end and notched their second of the afternoon when Adnan Januzaj found Van Persie. The Dutchman steadied himself and then fired the ball high into the net.
If that wasn't bad enough for Fulham, it soon got worse. Van Persie turned provider, rolling the ball to Rooney who gobbled up the chance.
Berbatov attempted to pull the Cottagers back into the match, but after turning Nemanja Vidic, his shot was saved.
Rooney then smashed the ball wide from 40 yards out.
Fulham managed to find a way back into the match through Alex Kacaniklic's shot, although it did take a deflection off Wayne Rooney.
Darren Bent almost grabbed Fulham's second but his header hit the top of the crossbar.