Sir Alex Ferguson's side wasn't particularly convincing in the narrow victory as Martin Jol's Cottagers battled without creating too many clear chances.
United began the stronger of the two sides, but after Fulham played its way back into the match, the home side opened the scoring just before halftime through Wayne Rooney.
The Red Devils dominated most of the second half and despite a number of chances, the club wasn't able to add to the solitary strike.
Ryan Giggs came in for Paul Scholes in the center of midfield to make his 903rd appearance, and Javier Hernandez droped to the bench as Ashley Young returned to the starting side.
Fulham made three changes from the side that lost 3-0 at home to Swansea in its last league fixture as Philippe Senderos was replaced by Aaron Hughes in defense, Damien Duff came in for Andy Johnson and Bryan Ruiz also lost his place to Kerim Frei.
The match didn’t take long to assume a fairly obvious pattern as United looked to pressure and attack Fulham from the first minute, but it took a little longer to create the first proper chance of the night.
Rooney had forced Mark Schwarzer into a comfortable save early on, but it was around the 10th minute when Giggs almost pulled off an unlikely feat as the Welshman headed Rafael’s cross goalwards.
Despite United’s dominance of the possession, Fulham wasn’t holding back when given the opportunity to attack, with Frei and Moussa Dembele looking very lively on the ball. The latter surged through the midfield before firing towards goal, but as has been the case with the Belgian this season his finish was wayward.
Soon it was Clint Dempsey who was getting forward. The American twisted and turned as he ran at Jonny Evans, then hitting a shot on goal, but David De Gea was able to gather it easily.
Clear chances were few and far between in the first half, but Patrice Evra put an audacious overhead kick just wide of Scharwarzer’s right hand post. Then Rafael presented the Aussie with an easy save as the right back shot with his left foot when a pass into the penalty area looked the better option.
The home side continued to have the better of the closing stages as it had a penalty shout turned down for a handball by Frei, but it didn’t matter as United took the lead four minutes before halftime.
Young delivered a right-footed cross from the left, but Fulham failed to clear it, allowing the ball to fall kindly for Evans. He, in turn, cut it back to Rooney for an easy finish. And despite a pretty poor performance, United went into the break in the lead.
Barely two minutes had been played in the second half before Valencia almost doubled United’s lead. Giggs placed a delicate pass over the Fulham defense for the winger to run on to, but his half-volley was saved by Schwarzer.
With about 15 minutes left, United had three chances in five seconds, as Young had a volley saved by Schwarzer from Valencia’s cross. He then reacted to the rebound, but Schwarzer again made the save and lastly Giggs volleyed that rebound towards the goal, and again Fulham was saved as Brede Hangeland managed to get in the way.
With United looking far from ruthless in attack, Fulham was perhaps sensing that a chance would be there and Dempsey almost got it as he stretched to reach a long ball into the area, but he couldn’t quite reach it.
As the match entered the final 10 minutes, it became clear the home team was looking to settle for the one goal lead as Rooney departed for Scholes, but Javier Hernandez, also a sub, did go close as he attempted to prod home Valencia's pass.
Fulham was adamant it should have been given a late penalty as Danny Murphy was tripped up from behind by Michael Carrick, but referee Michael Oliver wasn't interested and the club fell to yet another away defeat.
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