Cristiano Ronaldo's first-half strike kept Manchester United's slim hopes of catching runaway leaders Chelsea alive.
Ronaldo fired a 25-yard finish into the roof of the net after 21 minutes to give United a deserved victory.
Fulham rallied in the closing stages, but were denied a point when Lee Clark's shot hit the woodwork and Andy Cole's drive was deflected to safety.
United's victory margin should have been bigger, with Edwin van der Sar denying Wayne Rooney and John O'Shea.
United boss Sir Alex Ferguson selected an unchanged team for only the second time this season - and they responded by totally dominating the first 45 minutes against a desperately poor Fulham.
Paul Scholes headed narrowly wide as early pressure mounted, and it was no surprise when Ronaldo gave United the lead in spectacular style after 21 minutes.
The young Portuguese winger cut in from the left before unleashing a powerful 25-yard drive high past Van der Sar.
United spent the rest of the half on cruise control, without creating too many clear-cut opportunities to emphasise their superiority.
Wayne Rooney was always a threat, and he almost doubled United's lead on the hour when he had a shooting opportunity from long-range.
The teenager fired in a low and powerful shot, but Van der Sar plunged low to his left to save.
Fulham then suffered another blow when influential midfield man Papa Bouba Diop pulled up sharply with a hamstring injury and was replaced by Sylvain Legwinski.
Ronaldo was United's biggest danger, and he came within inches of adding his second after 67 minutes, firing a left-foot shot across the face of goal after being played in by Scholes.
Van der Sar then came to Fulham's rescue once more, diving inside his six-yard box to turn away Gabriel Heintze's dangerous cross.
Fulham's first moment of danger came with nine minutes to go, and were only denied an equaliser by the woodwork.
Clark's shot came back off the post, and United's previously unemployed goalkeeper Tim Howard need to dive to his right to block Carlos Bocanegra's drive from the rebound.
It would have been harsh on United - but punishment for their failure to take full advantage of their dominance.
Former United striker Cole then saw a close-range shot deflected narrowly wide off Howard's legs.
United substitute Alan Smith almost crowned the victory with a lob from the half-way line, but Van der Sar scrambled back to save.
Manchester United boss Sir Alex Ferguson:
"We were lucky late on when Fulham hit a post and Tim Howard saved from Andy Cole. It would have been ridiculous though.
"Our finishing play was really disappointing, but a win's a win.
"Cristiano Ronaldo was our best player and deserved his goal. He was the one who kept his performance level up."
Fulham boss Chris Coleman:
"In the last 15 minutes we were very good. We were only one goal down and holding our own, and had chances to equalise late on.
"We were going for it. They were getting edgy and I think if we show the same intensity against Portsmouth next time we will get a positive result.
"We need to beat teams in and around us and there were good things for us."
Man Utd: Howard, Brown, Ferdinand, Silvestre, Heinze, Ronaldo, Scholes (Phil Neville 90), Keane, Fortune, van Nistelrooy (Smith 77), Rooney (O'Shea 83).
Subs Not Used: Carroll, Gary Neville.
Goals: Ronaldo 21.
Fulham: Van der Sar, Rosenior, Knight, Goma, Bocanegra, Jensen (Radzinski 89), Malbranque, Clark, Diop (Legwinski 64), Boa Morte, Cole.
Subs Not Used: Volz, Crossley, John.
Ref: A D'Urso (Essex).