Two goals from Paul Pogba and a superb solo effort from Anthony Martial secured a comfortable win for the visitors, their 10th in 11 matches in all competitions under caretaker manager Ole Gunnar Solskjaer.
United, who kept player-of-the-month Marcus Rashford on the bench as they made six changes from the 1-0 win at Leicester City, were rarely troubled by a Fulham side who have now lost 23 of their last 24 league meetings with 'big six' opposition.
An encouraging start from Fulham saw Luciano Vietto scuff a volley wide from a promising position, and that miss was punished by Pogba 14 minutes in, the midfielder racing onto Martial's pass and blasting left-footed beyond Sergio Rico at the near post.
United seemed happy to invite Fulham onto them in order to strike on the break, and they did so in ruthless fashion 23 minutes in. Phil Jones won back the ball and released Martial, who burst forward while holding off Denis Odoi, skipped beyond Maxime Le Marchand and slotted past Rico.
Fulham were unable to make any inroads against the United defence, prompting Claudio Ranieri to shift formation by bringing on Cyrus Christie for Andre Schurrle, prompting cries of 'You don't know what you're doing' from the home fans.
Ander Herrera saw a half-volley beaten away by Rico as United pushed for a third, and they promptly found it from the penalty spot 64 minutes in, Pogba sweeping the ball into the right-hand corner after Le Marchand tripped Juan Mata.
United substitute Alexis Sanchez shot straight at Rico when clean through and then saw his cross nodded just over by Scott McTominay, while Fulham's best chance for a consolation goal fell to Ryan Babel, who somehow hit the outside of the post from practically on the goal-line, drawing a wry smile from his manager.
What does it mean? United back into the top four
This result means United will finish a day in the top four for the first time since they beat Leicester City on the opening day of the season, although Chelsea will climb above them if they beat Manchester City on Sunday.
It is an 11th league game without defeat against Fulham and marks the first time they have won six matches away from home in a row since May 2009.
While Solskjaer's men will be feeling buoyed ahead of a daunting run of games, Ranieri's side will sense the pressure building. They remain seven points from safety.
Martial too much to handle
Martial's runs from deep down the left were causing Odoi problems even before he set up Pogba's opening goal and scored a sublime second himself. It was a clinical, sometimes classy display from the Frenchman.
Le Marchand a mess
Fulham's continued defensive problems were underlined by Le Marchand's display. He made a lame attempt to stop Martial's run for the second goal and clattered into Mata to concede the penalty.
Key Opta facts
- Fulham have conceded 58 goals in 26 Premier League games this season; only three sides have shipped more at this stage in the history of the competition (Barnsley in 97-98 - 62, Swindon Town in 93-94 - 60 and Blackburn Rovers in 11-12 - 59).
- Solksjaer has picked up 25 points in the Premier League since taking over in December (W8 D1), more than any other manager has achieved in his first nine games in charge of a single club in the competition.
- Manchester United have scored seven goals from the penalty spot in the Premier League this season, more than any other side.
- Pogba has reached double figures for goals for the first time ever in a single league campaign (11).
- Martial has now been directly involved in 50 Premier League goals (33 goals, 17 assists) - more than any other United player since his debut in September 2015.
United host Paris Saint-Germain in the Champions League and travel for an FA Cup tie at Chelsea before their next league outing, at home to Liverpool on February 24. Fulham have 13 days off until they travel to West Ham for a London derby.