Despite dominating the first half and hitting the woodwork on four occasions, it looked as though they were going to be held to a 0-0 draw by their hosts.
However, in the closing stages Wayne Rooney kept his composure inside the area to give United all three points.
You can find out how the match unfolded with our minute-by-minute commentary below.
"The Cup game was quite comfortable," said the 27-year-old forward.
"But at home, Fulham are a different team. They have got players who can take the ball between the lines because the pitch is not as big and then they can create chances.
"They are down near the bottom so they will be fighting to get one or three points."
Fulham: Etheridge, Petric, Frimpong, Emanuelson, Davies, Kacaniklic, Hughes
Man United: Anderson, Giggs, Smalling, Chicharito, Welbeck, Kagawa, Amos
"There is a long way to go and a lot can happen. We're not certainties. Nobody is in this league. It's an unremitting league and if you make mistakes, you get punished."
"We knew that we had to play Man United on Saturday - every point against them is a bonus but we needed that win against West Ham."
"Raphael is wearing his brother Fabio's boots. Hopefully he didn't also pick up the wrong lunchbox this morning - he hates Fab's sarnies."
Will they be today? It's looking increasingly likely.