Paul Pogba fired United ahead from an impossibly tight angle in the 14th minute, springing in behind the defence and onto a pass from Anthony Martial on the left, turning and shooting first time between keeper Sergio Rico and the near post.
Martial doubled the lead nine minutes later in style, collecting the ball on the halfway line, jinking past Denis Odoi and racing all the way into the area before stroking his shot beyond the reach of Rico.
Belgian striker Romelu Lukaku had an anonymous first half, outshone by his two French team mates. But he helped create the penalty that led to the third goal when he charged forward to pass to Juan Mata, who was bundled over inside the area by Fulham's Maxime Le Marchand.
Pogba converted from the spot to put the game beyond Fulham's reach, and was then substituted, most likely to keep him fit ahead of a tough schedule in the coming weeks.
United face French champions Paris St Germain in a Champions League last-16 tie, Chelsea in the FA Cup fifth round, and host arch-rivals Liverpool all within the month.
The win at Fulham lifts United into fourth place in the league, ahead of Chelsea's visit to Manchester City on Sunday.
Fulham remain in relegation territory in 19th place, and they too have a tough schedule ahead. Yet to win away from home this season, their next three visitors at Craven Cottage are all powerhouses - Chelsea, Liverpool and Manchester City.