The visitors, in interim boss Ralf Rangnick’s penultimate game in charge before he is replaced by Erik ten Hag, fell apart in the second half, conceding three goals in quick succession.
Marc Cucurella fired into the roof of the net from Leandro Trossard’s pull-back for the second, with Trossard setting up Pascal Gross to calmly steer in a third.
The fourth goal was scored by Trossard when he bundled the ball over the line from close range, with the goal eventually given after a video assistant review checked for a handball.
The defeat was United’s fifth successive away loss and ensured they cannot finish higher than their current spot of sixth in the Premier League, with only the top four playing in next season’s Champions League.
It will be only the fifth time in 30 years that they will not play in Europe’s major competition – and they could even miss out on the Europa League and drop into the third-tier Europa Conference League.
They are currently six points ahead of seventh-placed West Ham, who have two games in hand.
Watch ‘Brighton 4-0 Manchester United – Goal Highlights’ Below