United stormed into a 3-0 lead inside the opening 22 minutes as Antonio Valencia, Robin van Persie and Wayne Rooney struck to take advantage of Fulham's inability to work the offside trap.
Fulham battled hard and grabbed a lifeline midway through the second half as Alex Kacaniklic's shot went in via a Rooney deflection, but United held on for a fourth straight win in all competitions.
Valencia was one of four players brought into the starting XI by David Moyes and he made an impact in the ninth minute as he slotted United into an early lead after Rooney had latched on to Van Persie's through-ball and committed a couple of defenders and the goalkeeper before selflessly squaring it.
Pajtim Kasami, full of confidence after his recent wonder goal, had tested David de Gea with a long shot before Fulham fell behind and Dimitar Berbatov then came close to an equaliser when Rafael got a crucial touch to prevent him from finishing off a Scott Parker pass.
However, the Cottagers were shambolic in defence and it was 2-0 to United after 20 minutes when Adnan Januzaj dispossessed Parker and skipped forward to release Van Persie. The flag again stayed down and the Dutchman slammed a powerful finish past Maarten Stekelenburg and into the roof of the net.
A third goal arrived just a couple of minutes later as Fulham were carved open by a simple ball from deep when Sascha Riether played Van Persie onside, and he had time to deliver a low cross for Rooney to turn home from close range.
Kieran Richardson had a shot from distance deflected wide and Berbatov forced a decent stop from De Gea after being played in by a nice Bryan Ruiz flick as Fulham tried to find a way back into the match.
The flow of the game was disrupted in the latter part of the first half by a series of injury scares as Patrice Evra, Rafael and Tom Cleverley all had to receive treatment.
All three made it through to half-time but Rafael and Cleverley then went off as part of a triple substitution at the interval, with Jonny Evans also replaced as Marouane Fellaini, Shinji Kagawa and Chris Smalling were given opportunities.
United struggled to reproduce the same kind of intensity and there were signs of improvement from the hosts as Kasami drilled wide from the edge of the area.
Nemanja Vidic demonstrated good command of his area to head away a threatening Kasami cross, while a penalty appeal was waved away after Parker had gone down under a Smalling tackle.
Fernando Amorebieta was yellow carded after a cynically late foul on Valencia on the counter-attack, before blocking a header from Fellaini at the back post from Rooney's free-kick.
Fulham's efforts were rewarded in the 65th minute when substitute Kacaniklic's low shot from 20 yards took a crucial deflection off Rooney to beat De Gea and reduce their arrears.
Januzaj showed glimpses of his exciting skill and had a shot saved by Stekelenburg from a tight angle, but it was Fulham who had the greater purpose as they attempted to retrieve what had looked an insurmountable deficit, and there was a nervy scramble in the United area as Richardson and Berbatov strikes were blocked.
Phil Jones also picked up a knock but had to play on and there were further anxious moments for United as Adel Taarabt had a shout for a penalty fall on deaf ears following a strong Vidic challenge and Darren Bent looped a header against the crossbar.
Richardson also headed wide, while at the other end Van Persie completely missed his kick when presented with a chance to score United's fourth.
Tempers flared in the closing stages as Riether stamped on Januzaj near the corner flag, but it did not sour a comfortable afternoon for United as they kept in touch with the Premier League leaders.