Five days on from being knocked out of the Champions League by Sevilla, the Red Devils were once again far from their best in an attacking sense but still got the job done on this occasion.
Jose Mourinho made a big selection call by leaving out Alexis Sanchez in one of five changes from the loss to Sevilla, but the fresh legs did not appear to bring fresh impetus in a bland opening quarter to the match.
From the resulting corner, the ball fell to the feet of Chris Smalling but he could only send it back off the outside of the upright after finally adjusting his feet.
Brighton enjoyed the odd spell of prolonged possession as they went in search of just a second win in 18 attempts against tonight's opponents, coming close to making a breakthrough when Lewis Dunk powered a header on target for Sergio Romero to push aside.
Lukaku gave the home side a lead to protect with eight minutes of the first half to play, though, by making the most of a fine first-time delivery from Matic at the back post to head the ball past Tim Krul.
United's record of having yet to concede in this season's FA Cup came under serious threat in the opening 15 minutes of the second half, as Pascal Gross's outside-of-the-boot attempt deflected inches wide and Romero was forced to make a few stops.
Chances continued to fall Brighton's way, most notably for Locadia who headed wide at the back post when picked out in a promising position.
Having failed to get a single shot away of any note between half time and the 83rd minute, United finally killed the game off when Matic watched Ashley Young's free kick all the way and guided it past Krul via his head.
Romero was being tested until the end, keeping out another couple of Gross shots, though in the end it was United celebrating a win that keeps them on course for a 13th triumph in this competition.
MANCHESTER UNITED (4-2-3-1): Romero; Valencia, Bailly, Smalling, Shaw (Young 46'); Matic, McTominay; Mata (Rashford 75'), Lingard (Fellaini 89'), Martial; Lukaku
BRIGHTON & HOVE ALBION (4-3-3): Krul; Schelotto, Duffy, Dunk, Suttner; Gross, Propper, Kayal; March (Izquierdo 68'), Ulloa (Murray 76'), Locadia