Dimitar Berbatov rounded off the victory with an audacious backheel in stoppage time after goals from Danny Welbeck, Nani, Ryan Giggs and Wayne Rooney.
"We played some superb football in the first half," United manager Alex Ferguson said. "It's not an easy place to come. We have experienced that in the last three years. We have got one point from nine here so that shows you the difficulties."
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The victory came at a cost, with defender Phil Jones forced off
injured in the 20th minute after being caught by Clint Dempsey's arm
while dueling for the ball.
And his replacement, Ashley Young, came off injured while tackling Dickson Etuhu at the start of the second half with an unspecified injury that Ferguson said will rule him out for two to three weeks.
"The tackle on Ashley Young was a very aggressive tackle and I will have to see that again," Ferguson said. "Fulham were very aggressive in the second half and Ashley Young has paid the price for that. He has got a sore one so will be out for two to three weeks."
"On Phil Jones it was an elbow from Dempsey, but I don't think it was intentional. But he caught him with an elbow. We are sending him for an X-ray tomorrow and it doesn't look great. We are picking up injuries at the moment."
United, though, are only two points behind neighbours City, who beat Stoke 3-0 at Eastlands.
Having failed to win on their past three visits to Craven Cottage, the Red Devils never looked in danger of extending that run on Wednesday.
Manchester United made one change to the side that defeated QPR in West London on Sunday, with Anders Lindegaard coming in to replace David de Gea. Meanwhile, Rooney astonishingly became the youngest-ever player in the Premier League to make 300 appearances at the age of 26 years and 58 days, eclipsing Gareth Barry's record of 26 years and 247 days set in 2007.
Danny Welbeck capitalized on lax defending to break the deadlock within five minutes. Patrice Evra fed the ball to Nani on the half-way line, and the Portuguese winger was allowed to run unchallenged to the byline before sending in a pass to an unmarked Welbeck to slot home, a soft, soft goal for the home side to concede so early in proceedings.
The hosts almost got back level after 20 minutes as Bryan Ruiz played a neat one-two with Dempsey on the edge of the area before bearing down on goal, only to be thwarted by a fantastic last-ditch tackle from Phil Jones who sent the ball out for a corner. It was to be the young defender’s last action of the match as he was substituted straight afterwards.
It didn’t seem to phase United, and the visitors extended their advantage when Nani nodded home a cross from Ryan Giggs.
The 38-year-old midfielder's performance in the capital belied his years and he extended his streak of having scored in all 20 Premier League seasons when he saw a drive deflect off Philippe Senderos and loop in two minutes before the break.
The home side were booed off the pitch at half-time, but looked resurgent after the restart.
Anders Lindegaard was forced into his first real stop of the match as he got down well to prevent a header creeping over the line, and a minute later Moussa Dembele went close, his shot drifting an effort just wide. John Arne Riise then saw a free-kick fade just wide after Danny Murphy’s lay-off.
Still, Antonio Valencia shot at David Stockdale as United pressed for a fourth goal, before Chris Smalling blocked former teammate Dempsey's goalbound effort at the other end.
Play swung from one end to another as the match entered the final 20 minutes, before Rooney capped a fine performance with a superb 30-yard effort two minutes from time that left Stockdale with no chance..
Substitute Berbatov finished the rout with a nonchalant backheel from Valencia's cross in the 90th minute.