Saturday evening's clash at Bramall Lane saw the Premier League's basement boys emerge victorious courtesy of David McGoldrick's early strike, somehow surviving a second-half Seagulls onslaught.
Too many times this term, the Blades have failed to take their chances when it mattered and seemingly ended up the wrong side of countless fine margins as a result of some serious misfortune.
But, on this occasion, they capitalised on one of only two decent openings created on the night, while at the other end, their own goal led something of a charmed life.
Following a fairly bright first-half showing, United were trapped inside their own territory for almost the entirety of the second 45, managing to sneak over the line thanks to some poor Brighton finishing and with the help of VAR.
Ultimately, however, they benefited from perhaps their boldest bit of play of the contest, which arrived when Albion defender Adam Webster carelessly gifted possession away and Enda Stevens' nicely-weighted pass sent Ben Osborn scampering clear down the Sheffield left.
The former Nottingham Forest attacker whipped a cross in with real intent, aiming to pick out the run of McGoldrick at the far post, and although a defender got their first, the ball only made it as far as Rhian Brewster, who showed more desire than Pascal Gross on the edge of the penalty area.
His touch diverted the ball into the path of McGoldrick, and he swept a low finish past Robert Sanchez with the minimum amount of fuss.
That moment aside, the opening period witnessed plenty of neat and tidy build-up play from both teams, though there was little by way of cutting edge on display.
The only other incident of note came with the match still goalless, the impressive Yves Bissouma playing Neal Maupay through on the home goal before John Fleck came to United's rescue with an excellent covering block.
The second half was an entirely different affair, with Brighton dominant throughout and creating a decent opportunity to draw level within 11 seconds of the re-start.
On that occasion, Adam Lallana stroked a tame effort from a good position straight at Aaron Ramsdale, who then produced a much better save to keep out Maupay's 54th-minute blast following some lovely interplay between Lallana and Danny Welbeck.
An equaliser looked very much on the cards by this stage of the game, and it appeared that one had materialised 60 seconds later.
A corner from the right was helped on by Welbeck, then by Webster, for Jakub Moder to eventually apply a finishing touch at the back post, only for VAR to intervene and rule the goal out for offside.
Undeterred, the visitors kept coming and Bissouma burst forward from midfield and shot narrowly wide of the upright from 20 yards before Welbeck directed a diving header past the post.
The Blades were visibly creaking heading into the last 20 minutes and should have finally been pegged back when Brighton substitute Alireza Jahanbakhsh produced an inviting centre from the right, which was met inside the six-yard-box by Maupay, who somehow cleared the cross-bar.
Paul Heckingbottom's team finally created a clear opening of their own in the 75th minute as George Baldock cut the ball back from the right, though Jayden Bogle only succeeded in poking a poor finish straight at Sanchez.
Desperate for a point in their own battle to avoid demotion to the Championship, the Seagulls kept pushing right until the end, but one diving stop from a long-range Jose Izquierdo effort aside, Ramsdale wasn't overly busy during the dying moments as United saw the game out.
Sheffield United: Ramsdale; Baldock, Egan, Bryan; Bogle, Norwood, Fleck, Osborn (Lundstram 81), Steves; Brewster(Burke 65), McGoldrick. Unused substitutes: Foderingham, Mousset, Lowe, Jagielka, Ampadu, Brunt, Gordon.
Brighton & Hove Albion: Sanchez; Webster, Dunk, Veltman; Gross (Jahanbakhsh 67), Lallana, Bissouma, Moder (Connolly 67); Trossard (Izquierdo 82); Maupay, Welbeck. Unused substitutes: Steele, MacAllister, Alzate, Propper, Zeqiri, Burn.
Referee: K Friend (Leicestershire).