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, which kept player-of-the-month Marcus Rashford on the bench as it made six changes from the 1-0 win at Leicester City, was rarely troubled by a Fulham side that has now lost 23 of its past 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 on to it in order to strike on the break, and it 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 was 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 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.
The result meant United finished a day in the top four for the first time since it beat Leicester City on the opening day of the season, although Chelsea will climb above it if it beats Manchester City on Monday (AEDT).