Ole Gunnar Solskjaer's side fell behind after just 13 minutes as Danny Welbeck once again found the back of the net against his former employers, with the Englishman seeing his header kept out by Dean Henderson before tapping home the rebound.
Brighton's defence stood firm and United's attackers had no answer to the Seagulls' resilience in the opening 45 minutes, although the hosts started to turn the screw during the early periods of the second half, and it paid off just after the hour mark.
A mistake by Joel Veltman allowed Bruno Fernandes to race forward and set up Marcus Rashford, who took it first time and curled an effort into the far corner to spark an upturn in United fortunes. The Red Devils' dominance eventually bore fruit in the 83rd minute as Mason Greenwood got his head to Paul Pogba's scuffed effort to seal the win for the hosts.
United have now consolidated their hold on second spot in the table, although they are still 14 points behind runaway leaders Manchester City, while Brighton remain in 16th - six points clear of the drop zone.
Manchester United now turn their focus towards the first leg of their Europa League quarter-final with Granada on Thursday, while Brighton have a full week to recover before they welcome Everton to the South Coast on April 12.
4th min: Bruno Fernandes gets the first shot of the game away, but his long-range effort is wide.
8th min: Relentless Man United pressure ends with Mason Greenwood picking the ball up just inside the area, and his low shot cannons back off the post.
13th min: Danny Welbeck returns to haunt his former club. The former Red Devils striker is picked out by Neal Maupay, and his initial header is kept out by Dean Henderson, but he is there to pounce on the follow-up. 0-1 Brighton.
38th min: United continue to struggle for clear-cut opportunities - Fernandes finds Paul Pogba on the edge of the area but he cannot get a clean connection.
45 + 1 min: An out swinging Gross corner finds its way to Jakub Moder, whose effort takes a slight deflection on its way past Henderson's post, and the second corner comes to nothing before the half-time whistle blows.
52nd min: Marcus Rashford chalks up Man United's first shot on target of the night from outside the area, but it is straight at Robert Sanchez.
60th min: Pogba plays a delightful first time ball into Fernandes, but Sanchez manages to smother the ball behind for a corner, which Dunk clears.
62nd min: United restore parity after a mistake from Joel Veltman. Fernandes races forward and manages to find Rashford just before being taken out, and the England international calmly curls an effort into the far corner. 1-1.
65th min: United begin to turn the screw and Mason Greenwood is picked out inside the area, but the youngster cannot direct his first-time effort on target.
69th min: A speculative effort from Fred takes a significant deflection, but it is enough to worry Sanchez before the ball eventually lands on top of his goal.
70th min: Welbeck is inches away from getting a foot on Maupay's cross, but the scorer thinks that he should have been awarded a penalty after going down under a challenge from Harry Maguire. Mike Dean waves away the protests before VAR upholds his decision.
76th min: The hosts are inches away from taking the lead after Sanchez parries Fernandes's effort into danger, and Greenwood's attempt at a follow-up dips onto the top of Sanchez's unoccupied goal.
80th min: Fernandes hits a tame effort from outside the area, and Sanchez has no problem gathering calmly.
83rd min: Solskjaer's side finally get the second goal they so crave. Fernandes picks out Pogba from the left, and the midfielder completely scuffs his volley, but Greenwood is on hand to head home after a deflection from Ben White. 2-1.
MAN OF THE MATCH - MASON GREENWOOD
There were some standout performances in midfield from Fred, Yves Bissouma and Adam Lallana, but the matchwinner Mason Greenwood was a menace throughout the 90 minutes and was eventually rewarded for his efforts late on.
The youngster put himself in harm's way to dive for the header which ultimately propelled United to all three points, and he could have easily had a couple more on the night. Another promising performance from Greenwood.
Danny Welbeck had a penchant for scoring against his former club while on the books at Arsenal, and the 30-year-old's habit of finding the back of the net at Old Trafford did not stop this time around.
The Brighton man showed plenty of desire to beat Aaron Wan-Bissaka and get his head on the ball, and he was well-placed to poke home the rebound after Henderson's initial save. A delight for Graham Potter to have the injury-plagued striker firing on all cylinders, even if his opener ultimately went unrewarded.
Possession: Man United 58%-42% Brighton
Shots: Man United 15-5 Brighton
Shots on target: Man United 7-3 Brighton
Corners: Man United 5-6 Brighton
Fouls: Man United 14-7 Brighton
MANCHESTER UNITED (4-2-3-1): Henderson; Wan-Bissaka, Lindelof, Maguire, Shaw; Fred, Pogba (McTominay 84'); Greenwood, Fernandes, Rashford (James 72'); Cavani (Van de Beek 82')
BRIGHTON & HOVE ALBION (3-4-1-2): Sanchez; White, Dunk, Veltman; Gross, Bissouma, Lallana (Zeqiri 87'), Moder (Jahanbakhsh 87'); Trossard (Mac Allister 63'); Maupay, Welbeck