Chris Hughton made two changes to the side that lost to Watford, with Gaetan Bong and Martin Montoya coming in for the injured Bruno and full-back Bernardo.
The Seagulls started the match on the front foot and in the 25th minute took a deserved lead.
The goal came when Solly March got down the left wing and put a low cross into the front post, which striker Glenn Murray flicked into the bottom right corner.
Brighton doubled their advantage in the 28th minute from a corner as Pascal Gross curled in a delivery which pinballed around in the box, before landing at the feet of Shane Duffy who swept the ball into the bottom left corner.
United pulled one back in the 35th-minute when the ball fell Luke Shaw on the edge of the box and his lofted ball into the box found Romelu Lukaku who headed home from two yards out.
Albion continued to push United and made it three before halftime when Dale Stephens won a ball in the midfield and played in Gross, who was brought down by Eric Baily.
Gross stepped up and fired the penalty into the roof of the net off David De Gea's outstretched left leg. Brighton came out and defended their two-goal lead well until the 94th-minute when substitute Marouane Fellaini was brought down by Duffy.
Captain Paul Pogba stepped up slotted the ball into the top right corner.
All Albion players put in a great shift
None of Brighton's players could be faulted for their efforts. From the first whistle to the final whistle they pressed United and put them on the back foot.
Add to this a near-packed crowd were cheering them on and creating such an incredible atmosphere, it made it a daunting task for Manchester United to get the upper hand in the game.
They struggled even further once they conceded a couple of quick goals in succession.
United failed to create any real chances from open play bar their opening goal.
In the second-half, Albion kept pressing and created two banks of four and made it hard to break them down.
United only had two chances which was a shot outside the box from Pogba which Matthew Ryan saved well.
The other was the penalty which Pogba scored in stoppage, however, this looked a bit of debatable decision with Fellaini looking like he was already on the way over before he was caught by Duffy.
Murray and Propper the two standout performers
There were two players that really stood out in their win over United. The first one was the sponsor's man of the match, Davy Propper.
Propper got stuck in the midfield and won the ball back on numerous occasions for the Seagulls in a battling performance well worthy of those man of the match honours.
He also tried to get Albion on the front foot after winning the ball back, but they, unfortunately, were just overhit for their intended targets.
The Brighton midfielder bossed the midfield and made a number of tackles, to thwart Pogba and others.
Then there was the goalscorer, Murray, who on his 200th appearance for The Seagulls and put in a classic Murray performance.
He opened the scoring in the 25th-minute when he made a trademark run in the box going across the front post before flicking into the bottom right corner.
Murray held up the ball well and battled against the likes of Bailly, Pogba and Victor Lindelöf.
He was substituted in the 91st minute, to a standing ovation by the Brighton faithful, who recognized the shift he put in.