Anthony Knockaert and Pascal Gross were standout performers for the Seagulls, and the latter scored the goal that ensures his side mathematically avoid relegation.
Brighton will have been disappointed not to have taken the lead going into the half time break, as the Seagulls had the best of the chances throughout the first period
They rode their luck just three minutes into the match, when Marouane Fellaini steered Marcus Rashford's free kick into the net, but the linesman had his flag raised from offside.
From that moment, it was all Brighton. They created their first good chance after 10 minutes when José Izquierdo could not convert a delicious cross from Knockaert.
Manchester United looked shaky in midfield, with Juan Mata in particular playing a few loose passes. Brighton carved out another great chance when Glenn Murray launched an ambitious shot from 30 yards and produced a stunning save from the strong right hand of David De Gea.
The Spaniard was forced into another great save soon after, when Izquierdo cut in from the left and De Gea had to tip his effort over the bar.
Between those two chances for Brighton, United's best opportunity came through Paul Pogba, but the Frenchman blasted his effort over the crossbar.
Knockaert then played in Pascal Gross, but De Gea produced another save with his legs to keep the scores level.
A passage of Manchester United play shortly before the half time whistle perfectly summarised the way the half went. Pogba made a dazzling run through the centre of the park, beating several players, but the former Juventus man failed to execute a simple pass at the end of the move, which summed up a disappointing night for the visitors.
United had the best of the build up play, but Brighton had the best chances in the opposition box and De Gea was by far the busiest goalkeeper.
United started the second half much stronger, looking to play balls over the top of the Brighton defence to utilise the pace of Marcus Rashford.
However, similarly to the first half, they could not create any great chances. The closest they got in the early stages of the second half was when Pogba saw his shot saved by Mat Ryan at the near post.
Just before the hour mark, Brighton broke the deadlock as José Izquierdo hooked the ball back for Pascal Gross. Marcos Rojo though he had cleared Gross' effort off the line, but referee Craig Pawson checked the goal line technology on his watch and pointed to the halfway line.
Despite the goal, United looked to continue their strong build up play. Pogba and Martial looked to connect on a couple of occasions, but again, they could not produce anything.
Juan Mata hit a free kick over the bar on 68 minutes, before Rashford forced a double-handed stop from Mat Ryan just minutes later.
Their clearest opportunity of the game arrived when Lingard and Rashford connected well, but the former fired his shot off target from just eight yards.
The tension around the Amex was clear for all to feel as the hosts knew that a win would mathematically confirm their Premier League status for next season, and they held on - deservedly - to get it
It was a sensational result for Chris Hughton's Brighton, who will now be a Premier League outfit next season. Meanwhile, defeat for United means the race for second place has creaked back open, with Spurs having the opportunity to go within three points on Saturday.
Next up for Brighton is a trip to face Manchester City at the Etihad Stadium, while Manchester United will travel to West Ham.