Sir Alex Ferguson's side weren't particularly convincing in the narrow victory as Martin Jol's Cottagers were denied a contentious penalty decision in the dying moments
United began the stronger of the two sides, but after Fulham played their way back into the match, the home side opened the scoring just before half-time through Wayne Rooney.
The Red Devils dominated most of the second-half and despite a number of chances, they weren't able to add to their solitary strike, but they held on despite a late penalty claim for Martin Jol's team as the Cottagers pressed for a late equaliser.
Last time out Manchester United hammered Wolves 5-0 at Molineux, but Sir Alex Ferguson still decided to make a couple of changes. Ryan Giggs came in for Paul Scholes in the centre of midfield to make his 903rd appearance, and Javier Hernandez dropped to the bench as Ashley Young returned to the starting eleven.
Fulham made three changes from the side that lost 3-0 at home to Swansea in their last league fixture as Philippe Senderos was replaced by Aaron Hughes in defence, 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 them 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 opened the scoring when heading Rafael’s right-wing cross goalwards, but Schwarzer was able to deal with it.
Despite United’s dominance of the possession, Fulham weren’t holding back when given the opportunity to attack, with Frei and Moussa Dembele looking very lively on the ball, and the latter surged through the hosts’ 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.
With 23 minutes played, Fulham had certainly got themselves into the contest after a slow start, as Frei cut in from the left before finding Dempsey, whose curling effort was spectacularly saved by De Gea. United were looking far from convincing as the half progressed.
Clear chances were few and far between in the first 45 minutes, but Patrice Evra put an audacious overhead-kick just wide of Schwarzer’s right hand post, and then Rafael presented the Australian 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 hosts continued to have the better of the closing stages as they had a penalty shout turned down for a handball by Frei, but it didn’t matter as they 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, who 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 defence for the winger to run on to, but his half-volley was saved by Schwarzer.
Next to test Schwarzer was Young, as the England winger cut inside before attempting to curl a right-footed strike into the bottom far corner, but the goalkeeper got down well to his left to palm it away.
The pattern of the second-half was similar to the first period, but United weren’t letting Fulham back into the contest particularly easily, keeping control of the possession and the match in general, rather than becoming complacent.
Rafael was continuing to look dangerous as he roamed forward, and approaching the 70 minute mark he spotted a gap and squirmed through, with the ball eventually falling to Giggs on the edge of the box, but his strike was poor and went comfortably wide.
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, but again Fulham were saved as Brede Hangeland managed to get in the way.
With United looking far from ruthless in attack, Fulham were perhaps sensing that a chance would be there for them, and Dempsey almost got it as he stretched to reach a long ball into the area, but he couldn’t quite reach it, luckily for the hosts.
As the match entered the final ten minutes, it became clear the home team were looking to settle for their 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, but the sting was taken out of his effort by a deflection.
Fulham were adamant they 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 they succumbed to yet another away defeat.