When they won promotion to the best league in the world, the Blades and their manager Paul Heckingbottom knew there would be halves – even games – like this, and they key was not to let it discombobulate them.
For all that the Seagulls are good to watch, they can sometimes struggle to put you out of sight, and this was one of those days.
But when the opportunity presented itself, courtesy of Mahmoud Dahoud's 69th-minute moment of madness, the Blades were still in the game, only a goal behind, and seized their opportunity.
Heckingbottom revealed afterwards Auston Trusty being so high up the field was not part of a masterplan but over-excitement on the defender’s part but from high in midfield he found Gustavo Hamer, who helped the ball to Jayden Bogle.
The wing-back drilled the ball across and Adam Webster put through his own net. Had he not, Cameron Archer would surely have tapped in.
A game the Blades looked set to lose comfortably ended 1-1, taking the visitors off the bottom of the Premier League and securing their first away point of the season in the process.
At times in the first 45 minutes, the Blades were as exposed as Luke Thomas, Brighton ripping holes in their defensive set-up as easily as the wing-back had in his flimsy shorts.
Brighton's early plan seemed to centre around overloading the Blades left-hand side with a lopsided formation which had a right wing-back in Pascal Gross doubling up with right winger Facundo Buonanotte, but no equivalent on the left.
So it was ironic, but not unconnected that the opener came down the opposite side just six minutes in.
When the Blades lost the ball in the centre of the park Brighton switched it out to Simon Adingra on the left and he played a one-two with Buonanotte, freed up to drift into a centre-forward position. With Trusty at his back, he cleverly flicked into the path of Adringra, moving in off the flank, to find the net.
From there, the hosts – buoyed by a midweek win over Ajax which coach Roberto de Zerbi had called the best in his club's history and which had clearly lifted spirts before the game – were able to stroke the ball around at will as the away side tried to work out best how to plug the gaps without negating the threat of Hamer by asking him to do too much defensively.
With the Blades offering negligible threat and failing to get in their faces, there was no pressure on the Seagulls to force the pace.
Brighton had 71 per cent of the first-half possession but only six shots to show for it, although they were accurate with it, putting four of them on target. It was four more than the Blades managed before the break.
In the 15th minute Adam Lallana played an excellent ball to Ansu Fati, but Wes Foderingham was off his line to deny the Barcelona loanee.
When Vinicius Souza was forced to head a deep Gross free-kick behind for a corner it found its way to Billy Gilmour, the deepest defender, and he played it back for Bounanotte to hit a shot into the side netting.
As the half went on Thomas got a new pair of shorts and the Blades got an overdue sight of the other end of the field but Bogle could not control his volley and when Jan Paul van Hecke gifted him the ball, Hamer's pass was just out of Archer's reach.
The half ended with Foderingham tipping over a shot from Gilmour, presented the ball by the goalkeeper's punch.
A double half-time substitution gave the Blades another threat to deal with and it took them a while to becalm Kaoru Mitoma on the left, fellow substitute Joao Pedro unable to keep his shot down and Jack Robinson put a big tackle on him.
Both chances were made by the Japanese forward, who then forced a near-post save.
But Dahoud's stamp on Ben Osborn was like finding a key you thought you had lost, and the Blades eagerly rushed through the door.
Level inside five minutes thanks to Bogle’s cross, the Blades pushed forward in search of a winner.
Bogle could not get a clean touch on his shot when Archer cleverly flicked a James McAtee pass into his path, Oliver Norwood having a shot blocked, and Thomas put an effort over.
It left gaps at the back but video assistant referee Chris Kavanagh correctly backed up John Brookes' decision that Thomas's foul on Baleba was outside the penalty area, and Osborn's proximity meant no need for a red card.
If ever point was hard earned, this was it as the Blades reaped the rewards of keeping their heads under pressure.
Brighton and Hove Albion: Steele; Webster, van Hecke, Julio; Gross, Gilmour (Baleba 71), Dahoud, Lallana (Mitoma 46); Buonanotte (Joao Pedro 46), Fati (Veltman 71), Adingra. Unused substitutes: Verbruggen, Moder, Hinshelwood, Baker-Boaitey, O’Mahony.
Sheffield United: Foderingham; Baldock, Trusty, Robinson; Bogle (Osula 90+5), Souza (Osborn 2), Norwood, Thomas; McAtee (Slimane 84), Hamer, Archer. Unused substitutes: Lowe, Fleck, Traore, Larouci, Brooks, Amissah.
Referee: J Brooks (Melton Mowbray).