The hosts made two changes from the side that saw West Ham in their last Premier League fixture. Paul Pogba and Edinson Cavani came in for Scott McTominay and Daniel James, while Dean Henderson started his seventh straight game in goal.
Manchester United had the first goalmouth action of the game after Mason Greenwood hit the post in the ninth minute, but the visitors went ahead soon thereafter.
Former Manchester United man Daniel Welbeck came back to haunt his old side when he rose highest to head home a cross by Neal Maupay. Dean Henderson pulled off a stunning save to deny him from point-blank range. Welbeck, however, reacted quickest to the rebound to put the Sea Gulls ahead.
Manchester United struggled to get going for the rest of the first half and did not register a single shot - the first time this happened in a Premier League game this season.
The second half saw the hosts up the ante. They got a deserved equaliser when Bruno Fernandes teed up Rashford to beat Robert Sanchez from 15 yards out.
There were calls for a penalty when Welbeck went down under a challenge in the box in the 71st minute, but referee Mike Dean waved play on. He maintained his stance after a VAR intervention.
Manchester United went close soon thereafter through Greenwood, whose shot on the rebound went narrowly over.
Greenwood was, however, not to be denied seven minutes from time, as he headed the ball home from Pogba's cross to put Manchester United ahead.
The hosts held on for the win to move back to within 14 points of table-toppers Manchester City. It also means the Old Trafford outfit have now picked up 25 points from losing positions this term, which is nine points more than anyone else in the league.
On that note, let's have a look at the Manchester United player ratings.
Dean Henderson - 6.5/10
Dean Henderson showed great reflexes to keep out Danny Welbeck's initial header but could do nothing about the follow-up. He had a jittery moment when he made a hash of a routine catch, but other than that, he was solid, if not spectacular.
Luke Shaw - 8/10
The Manchester United left-back had another solid game and was a key presence in both halves of the field. The 25-year-old had a 91% pass accuracy, two interceptions and created one chance.
Victor Lindelof - 6/10
The Sweden international was the weakest link in the Manchester United defence, as Victor Lindelof failed to effectively cover Welbeck.
Harry Maguire - 7/10
It was a solid display at the heart of defence for the Manchester United captain. Harry Maguire made three interceptions and had six clearances.
Aaron Wan-Bissaka - 6.5/10
Unlike Shaw, Aaron Wan-Bissaka did not offer much going forward. His crosses left a lot to be desired, and he not have too much defensive work to do as well.
Fred - 6.5/10
Fred was effective in his role as the screen for the defence, making three tackles on the night, in addition to one interception and two clearances.
Paul Pogba - 8/10
The Frenchman was immaculate on his return to the Manchester United starting lineup. Paul Pogba ended the night with the match-winning assist and also put in a defensive shift alongside Fred.
Marcus Rashford - 7/10
Marcus Rashford scored the all-important equaliser for Manchester United. He constantly put the visitors on the backfoot with his direct running before he was substituted in the 72nd minute with a suspected injury.
Bruno Fernandes - 8/10
The Manchester United talisman struggled to make a mark for most of the game, as he was hounded around by Yves Bissouma. Bruno Fernandes still managed to provide the assist for his team's equaliser and also played a key role in the buildup to the second. He created a game-high four chances and had three shots on target as well.
Mason Greenwood - 7.5/10
Following his early strike off the bar, Mason Greenwood was anonymous for most of the game until the final 15 minutes. He showed great awareness to score the match-winning goal and also received a late yellow for time-wasting.
Edinson Cavani - 6/10
The Uruguay international was on the periphery throughout his time on the field, as a resolute Brighton defence kept him at bay. Edinson Cavani was shown a yellow card in the 63rd minute and substituted in the 82nd, despite the hosts needing a goal.
Ratings of Manchester United substitutes
Daniel James - 6.5/10
Daniel James came on for Rashford in the 72nd minute and ended his night with one chance created for his teammates.
Donny Van de Beek - 6/10
Donny Van de Beek came on with eight minutes to go and produced a routine display.
Scott McTominay - 6/10
Scott McTominay Was brought in after the second Manchester United goal was scored to provide an extra body in midfield.