Sir Alex Ferguson's side continued the form they showed up the road at QPR on Sunday to secure three points that keeps them in touching distance of their rivals heading into Christmas.
United had failed to win on their past three visits to Craven Cottage but never looked in danger of extending that run tonight, ending their hoodoo thanks to an imperious display.
Danny Welbeck capitalised on lax defending to break the deadlock within five minutes and the visitors extended their advantage when Nani nodded home a Ryan Giggs cross.
The 38-year-old's performance in the capital belied his years and he became the first player to score in all 20 Premier League seasons when he saw a drive deflect off Philippe Senderos and loop in two minutes before the break.
Late goals from Wayne Rooney and Dimitar Berbatov extended the visitors' lead further, although it was not to be a perfect night for Ferguson due to injuries to Phil Jones and Ashley Young.
Fulham manager Martin Jol named an unchanged starting line-up for tonight's match, while Ferguson made minor alterations to the side that overcame QPR.
Anders Lindegaard started in goal for United and Giggs came in for Rio Ferdinand, who was left out of the squad altogether.
Jones dropped into defence as a result but was on the deck inside two minutes after being caught by a Clint Dempsey's wayward arm.
The England international was back on his feet after some treatment and soon had something to cheer about as United broke the deadlock.
Nani burst down the left flank, galloping the length of the Fulham half before producing a superb low cross that unmarked Welbeck tucked away with ease.
Fulham - playing their 32nd competitive match of the season - eked out their first opportunity in the 20th minute when Bryan Ruiz was put through by Dempsey.
The pair linked up for both of the Cottagers' goals in Saturday's 2-0 defeat of Bolton but were denied another thanks to an incredible Jones challenge, thwarting the Costa Rica international in the six-yard box.
The tackle was Jones' last action of the match as he immediately left the field, seemingly due to the earlier challenge with Dempsey.
Ashley Young came on but United looked unfazed and looked to extend their lead, soon conceding the goal that United had threatened.
Giggs played a short corner to Antonio Valencia and after receiving a return pass floated in a superbly-weighted cross, which Nani directed past Stockdale in the 28th minute.
United continued to press forward in numbers as the Cottagers struggled to cope, with Senderos looking particularly out-of-sorts and almost giving away a penalty for a mistimed challenge on Welbeck.
The former Arsenal defender was guilty of leaving Welbeck free for the opener and saw a first half to forget compounded two minutes before the break.
Nani was given acres of space to deliver the ball to Giggs, whose low drive deflected off Senderos' legs and looped over the backpedalling Stockdale.
The home side were booed off the pitch at half-time and, whether it was that or a half-time pep talk from Jol, Fulham looked resurgent after the restart.
Lindegaard and Evra combined to prevent a Dempsey header sneaking in, before Mousa Dembele and John Arne Riise came close with long-range drives.
Fulham's added impetus saw tensions begin to rise and the home support felt aggrieved that Dickson Etuhu was adjudged to have fouled substitute Young in a 50-50 challenge.
While referee Mark Halsey's decision irked the majority inside Craven Cottage, the England winger undoubtedly came off worse and had to be replaced by Park Ji-Sung.
Valencia stung the palms of Stockdale as United pressed for a fourth goal, before Chris Smalling blocked former team-mate Dempsey's goalbound effort at the other end.
Play swung from one end to another as the match entered the final 20 minutes, before Rooney capped a fine performance with a superb 30-yard effort two minutes from time.
Substitute Berbatov finished the rout with a nonchalant backheel from Valencia's cross in the 90th minute.