With five minutes to go, the 10 Bladesmen were on the verge of a historic Christmas repeat, getting their first win of the season on the weekend before the big day, just as they had against Nottingham Forest in 1990.
Aaron Connolly's 84th-minute header over an empty net seemed like confirmation that at last luck had turned their way and Premier League debutant Jayden Bogle had come off the bench to earn them three points.
Then Danny Welbeck crushed them with an 87th-minute volley.
Both sides could have won the game in the final, frantic minutes and both needed to – the Seagulls to get their first home win in this season's Premier League, the Blades to get their first anywhere this season. A 1-1 draw which doubled their points tally was scant consolation for their efforts.
All 22 players looked as downbeat as they were exhausted at full-time.
In all the talk about whether the Blades should drop the 3-5-2 formation that has been behind their unexpectedly rapid rise up the divisions, no one suggested 4-4-1, but they were better after John Lundstram was sent off late in the first half than before it, and were rewarded with Bogle's deflected goal.
Making life harder for themselves has been the sob story of their season, and they managed it again.
Jack Robinson was a magnet for the Blades' first-half problems but the man in front of him was struggling too, and when manager Chris Wilder – who played against Forest in 1990 – took John Fleck off to try to be more positive, a moment's recklessness from Lundstram saw that planned ripped up inside six minutes.
The midfielder launched himself into a tackle on Joel Veltman six minutes before half-time. You could hear the thump of foot on ball but it was also obvious he had launched himself in a way that is just not allowed nowadays.
Peter Bankes showed a yellow card but it always felt like a holding decision whilst video assistant referee Michael Oliver took another look. When he did, he told Bankes to go over to the pitchside monitor.
After winning the ball, Lundstram's foot speared down, studs first, just above Veltman's and a red card was the correct decision. When Bankes showed it, the Blades had lost both their attacking midfielders in no time at all.
Wing-back Veltman did not reappear for the second half.
It must have been a close run thing for Wilder whether to take off Robinson or Fleck. Had five substitutes not been again voted down in last week's Premier League meeting – with the Blades in the half of the division opposed – they might even both have been withdrawn.
An early Robinson long throw-in across his defence had put Chris Basham under pressure but the centre-back did well to win the ball back after Aaron Connolly nicked it.
Robinson's free-kick kicked off a 20th-minute counter attack although his ball into Fleck's feet was not a risk to a Premier League-quality midfielder, even with a man at his back. Unfortunately, Fleck's first touch was not Premier League-quality, and the move end with Adam Lallana's shot deflecting wide.
Three minutes later Robinson's header was indecisive and he was outmuscled trying to win it back, leading to Connolly shooting at Aaron Ramsdale.
With Basham blocking an Yves Bissouma effort, and Ethan Amapdu adding to the confusion to do likewise as Neil Maupay and Lewis Dunk got in each other's way at a corner, the Blades were firmly against the ropes.
Wilder decided to come out swinging, withdrawing a surprised and not injured-looking Fleck to introduce Oliver Burke as a third striker. Quickly afterwards McGoldrick, now in the hole of a 3-4-1-2, forced a good low save at a free-kick but before the formation had time to bed in, Lundstram was dismissed.
By the start of the second half, three forwards had become one, Burke and McGoldrick on either side of a midfield four. With Bogle introduced to it alongside Basham, centre-back-cum-midfielder Ampadu was the nearest thing to a specialist in there.
It worked a treat, McGoldrick laying the ball back for Bogle's deflected strike after 63 minutes.
For a long time it looked like Sheffield United might hang onto it, bringing Ben Osborn for McGoldrick to try to do just that. Solly March had a shot deflected, Adam Webster a header saved, Ramsdale rushed off his line to deny Connolly and when the striker somehow headed Aklireza Jahanbakhsh's cross over in the 82nd minute, it looked like an equaliser was not coming.
Two minutes later the Blades ought to have put Brighton to bed but when Osborn played Burke in, he blazed wide.
The Blades were punished once, nearly twice, with Jahanbakhsh hitting the frame of the goal in a stoppage-time scramble following Welbeck's equaliser.
Yet again, Wilder's men emerged with credit but not a win. This story is starting to get a bit boring.
Brighton and Hove Albion: Sanchez; White (Zeqiri 72), Dunk, Webster; Veltman (Jahanbakhsh 46), Lallana, Bissouma, March; Trossard, Maupay (Welbeck 66); Connolly.
Unused substitutes: Mac Allister, Gross, Alzate, Steele, Burn, Mollumby.
Sheffield United: Ramsdale; Basham, Egan, Robinson; Baldock, Lundstram, Ampadu, Fleck (Burke 33), Stevens; Brewster (Bogle 54), McGoldrick (Osborn 70).
Unused substitutes: Sharp, Mousset, Lowe, Jagielka, Norwood, Verrips.
Referee: P Bankes (Liverpool).
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