VAR intervened to deny John Egan and Jack O'Connell either side of half-time, however with Oliver McBurnie on target in the 23rd minute, the Blades left the south coast with all three points.
It extended their unbeaten away league record this season to nine games and they were rarely in danger during a one-sided clash played in relentless drizzle at the Amex Stadium.
Brighton were awful, particularly in defence, and even during the final 20 minutes when they poured forward in search of the equaliser they made mistake after mistake.
Had Republic of Ireland striker David McGoldrick been less wasteful - he missed an open goal - United would have emerged comfortable winners.
There could be no complaint at the application of VAR in the eighth minute as referee Robert Jones awarded Egan a goal that was quickly ruled out.
Egan bundled home a corner that was completely missed by keeper Mathew Ryan but replays revealed it came off the arm of United's Irish defender.
It then became Brighton's turn to have a goal chalked off and on this occasion Neal Maupay was frustrated by the off-side flag having completed a simple tap-in.
The third goal was allowed to stand, however, and the Seagulls only had themselves to blame after Adam Webster was guilty of lamely heading a clearance of a goal-kick into the path of McBurnie.
McBurnie still had the challenge of Lewis Dunk to hold off but his strength took care of that task and when the target opened up before him he drilled the ball into the bottom left corner.
It was a superb goal but Brighton's defence should have dealt with the route-one attack with ease and it was a sign of things to come as errors compounded in the face of United's persistence.
Despite enjoying most of the possession and territory, they could make no meaningful impact on Chris Wilders' team with their attack barely firing a shot.
In a bid to induce a response, Aaron Connolly and Glenn Murray were sent out for the second half at the expense of Leandro Trossard and Pascal Gross, but Brighton continued to blunder as another defensive lapse offered up a gilt-edged chance.
Webster was exposed once more but having done the hard part on shaking off the defender and rounding Ryan, McGoldrick found the side-netting with an open goal before him.
The pressure continued and VAR came to Brighton's rescue once again as O'Connell found the net after Ryan palmed a free-kick into his path only for off-side to be called.
United should have been protecting a comfortable lead but instead they came under sustained barrage as they defended furiously inside their own area without keeper Dean Henderson having a save to make.
Henderson had his first significant save to make in the 71st minute but he was able to palm a firm shot by Connolly over the crossbar.
McGoldrick missed another chance - although this was far harder than his previous one - before Brighton's last attack of note ended with Yves Bissouma being booked for a dive.
Brighton: Ryan, Montoya (Bissouma 56), Webster, Dunk, Burn, Pröpper, Stephens, Mooy, Groß (Murray 46), Trossard (Connolly 46), Maupay.
Sheffield United: Henderson, Basham, Egan, O'Connell, Baldock, Lundstram, Norwood (Besic 82), Freeman (Osborn 53), Stevens, McBurnie (Mousset 63), McGoldrick.
Report by PA.