Lukaku's close-range finish was his first at Old Trafford for 997 competitive minutes and followed efforts from Ashley Young and Juan Mata inside the opening half hour.
Claudio Ranieri's team lived down to the reputation of the Premier League's bottom club and any encouragement from Aboubakar Kamara's 67th-minute penalty was extinguished by Andre-Frank Zambo Anguissa's red card 47 seconds later.
Marcus Rashford completed United's first win in five league games, achieved with Paul Pogba as an unused substitute, which lifts the Red Devils to sixth.
Young did a fine job of lifting the prevailing mood at Old Trafford by nutmegging Denis Odoi on the left in the 13th minute and arrowing a superb strike into the top-right corner.
Lukaku's pass cut Fulham apart down the same flank and Mata's finish through the legs of Tim Ream matched the precision of Rashford's cutback – the England forward whose venomous free-kick was well saved by Sergio Rico in the 38th minute.
Unfortunately for the Fulham goalkeeper, the defensive efforts in front of him remained woefully tepid and Lingard released Mata to give Lukaku a simple finish before half-time.
Rico bravely threw himself at Lukaku's feet to save following a teasing cross from Diogo Dalot early in the second half.
Chris Smalling departed through injury, doing little to knock United out of their stride as Ander Herrera side-footed narrowly wide.
The Spanish midfielder was then harshly adjudged to have fouled Kamara, who converted from the spot.
Hopes of a Fulham revival were short-lived as Anguissa challenged Rashford untidily and was shown a second yellow card.
The overworked Rico saved well from Rashford and Lukaku after the introduction of Fred as a substitute. Given those stops, it was somewhat galling when Rico patted Rashford's speculative 83rd-minute effort into the net.