Ryan Giggs set United on their way with a third-minute penalty before a Wayne Rooney strike and a brace from Javier Hernandez sealed Fulham's fate in the second half.
It was always likely to be a tricky afternoon for the visitors and their task looked a lot tougher when Aaron Hughes - the scorer of a late consolation - handballed in the box after just 72 seconds.
Referee Mark Clattenburg pointed to the spot and Giggs duly converted despite fellow veteran Mark Schwarzer getting a firm hand to the ball.
United could and should have had a second penalty when Damien Duff clearly prevented a Giggs chip finding Patrice Evra but Clattenburg inexplicably ignored the appeals.
Fulham enjoyed plenty of possession with former Old Trafford favourite Dimitar Berbatov showcasing his usual delightful touches alongside the classy Bryan Ruiz.
But there was little threat in behind the home defence and Rooney had the best chance to double the lead before the break only for Schwarzer to save his effort onto the crossbar.
If Fulham were fortunate to get to the interval just a goal behind then any hope of clawing their way back into it ended quickly in the second half.
Anderson threaded a pass through to Rooney just five minutes after the break and the England forward cut inside onto his left foot to blast the ball past Schwarzer.
Rooney then turned provider for Hernandez to put the ball away from close range as United swamped their opponents.
And the Mexican had his second midway through the second half when he seized onto a pass from Giggs and saw his effort deflect off Hughes and squirm past the Fulham keeper at his near post.
Martin Jol's men pulled one back when Hughes headed in a Giorgos Karagounis corner at the near post but there was no way back for Fulham and it's United that take up their place in the last 16.