The Blades had fought back from 2-0 down to level at 2-2 through goals from Gus Hamer and Will Osula before the break, before Joao Pedro sealed his hat-trick with two more goals in the second period.
Pedro scored twice from the penalty spot, both spot-kicks conceded by Jayden Bogle, before sub Danny Welbeck capped victory with a fifth deep into stoppage time which squirmed through the grasp of Blades debut goalkeeper Ivo Grbic.
United can now at least put full focus on their Premier League survival bid, with Crystal Palace next up for the Blades on Tuesday night. Here's how we rated Chris Wilder's side as they tumbled out of the FA Cup...
5. Rhys Norrington-Davies 5
Given another start in the FA Cup after his long injury absence but was sold rather than spectacular before being replaced by Larouci in the second half. More valuable minutes in the legs for a key player | Sportimage
6. Ollie Norwood 5
Given a chance to impress in midfield and snapped into an early tackle to earn a yellow card with just 10 minutes on the clock, leaving him walking a tightrope for the rest of the game. Like the rest of United's midfield, had a tough afternoon against Brighton's technical players as they looked to move United around with their intricate passes. Should have had an assist from a corner but Trusty headed wide when it looked easier to score . Missed a tackle late on as Welbeck raced away to put the result beyond any conceivable doubt | Getty Images
7. Gus Hamer 7
Started brightly with a nutmeg and then a superb low cross that was only just cut out by the Brighton defence before Archer could get on the end of it. Had a great chance to equalise after Osula's effort was blocked but Julio did superbly to get across and get his body in the way of the shot. Got his goal eventually with a smart finish for 2-1 before picking up his customary 'pull-back' booking for the slightest of tugs on Gross as he looked to get away. Looked lively and was for my money United's best player before making way | Getty Images
8. Ben Osborn 5.5
Looked surprised to be presented with an opportunity inside the first few minutes inside the Brighton box as United pressed high and forced the mistake at the back, but Osborn's touch let him down and he couldn't capitalise. Almost made amends with a superb pass to send Osula free but the striker dallied and saw his shot blocked. A display full of energy as ever from the midfielder before he was replaced just after the hour mark | Getty Images