Ralf Rangnick's side put up little-to-no fight from the whistle, and went a goal down early when Moises Caicedo opened the scoring for Brighton.
United have now conceded more goals than in any other league campaign, with the defeat guaranteeing their worst Premier League-era points tally.
The win was Brighton's first at home since Boxing Day and puts them ninth in the table as they look to secure their first-ever top-half finish in the Premier League, while United remain sixth.
Brighton got off to a fine start and were rewarded after 15 minutes when Caicedo opened the scoring with a clinical finish through Victor Lindelof's legs.
The hosts were unlucky not to double their lead just before the break when Danny Welbeck pounced on Raphael Varane's scuffed clearance with David de Gea off his line. However, the former England international lifted his attempt agonisingly over the bar.
Rangnick switched things up after half time, bringing on Fred and Edinson Cavani in place of Anthony Elanga and Nemanja Matic but this did not prevent Brighton finding a second on 49 minutes through Cucurella. The Spaniard picked up a Leandro Trossard cross in space, drilling the ball past De Gea and into the roof of the net.
Pascal Gross added a third on 57 minutes from a superbly worked link of play that started with Roberto Sanchez from the back and ended with the German flicking the ball into the bottom-right corner after Cucurella and Trossard worked it up the pitch.
United's collapse was evident as Brighton made it four just three minutes later, with Trossard bundling in from close range after Diogo Dalot initially cleared a Welbeck chip off the line.
United looked to have scored a consolation on 72 minutes when Harry Maguire headed the ball goalwards for Cavani to poke in the ball, but the forward was deemed to be offside and the goal was disallowed to leave Brighton with a clean sheet.