Albion learnt the hard way that they cannot perform for only 45 minutes to pick up results in the Championship.
A tardy first half condemned Mark McGhee's side to their second home defeat of the season against the leaders.
Withdean has been something of a graveyard for pace-setting teams in recent seasons but Phil Jagielka's first half goal ensured United reversed the trend.
The Seagulls rallied after the break and arguably deserved a point.
But you cannot afford to give a quality outfit like the Blades a head start if you are going cut them down.
United manager Neil Warnock had obviously done his homework. Denied space in midfield, Albion struggled to supply their recently rampant front quartet, although McGhee questioned the work ethic of his team in the first half.
That will have to be corrected for Saturday's more winnable home match against Micky Adams' Coventry.
The former Albion manager, who was in the crowd last night, is bound to have them motivated for his return to Withdean.
French left-winger Alexandre Frutos, Albion's transfer window signing from Metz, got his first taste of English football from the bench at the expense of Alexis Nicolas, the only change to the squad.
A knock restricted Brighton-born Albion fan Paul Ifill to a substitute's role for Sheffield United, Northern Ireland international Keith Gillespie taking his place.
The visitors were also forced into a reshuffle in defence, Rob Kozluk coming in for the injured Craig Short with Leigh Bromby moving from rightback to the centre of defence.
This arguably suited United, Bromby's younger legs being better equipped to handling Albion's lively attack than the veteran Short.
Wayne Henderson launched Leon Knight's opening goal at Leeds on Saturday with a catch and quick throw from a corner.
We saw something similar from the visitors early on, Paddy Kenny catching a free-kick from Paul Reid and releasing Quinn for a lung-bursting surge down the left. His run ended with an angled shot which Henderson pushed away at his near post.
It was refreshing to see four out-and-out wingers on the pitch. The problem for Albion for much of the first half was that they did not have enough possession to feed Sebastien Carole and Albert Jarrett.
United's wide men were more prominent, Gillespie latching on to a poor clearance from Paul McShane for a shot which deflected off Albion's on-loan Manchester United centre half and just wide of the far post.
The table toppers' enterprise was rewarded with a 25th minute lead after Jagielka played a neat one-two with Steve Kabba. His first shot from inside the area was blocked by Henderson but the midfielder found the roof of the net from the rebound as he fell.
Kenny was relatively untroubled by the Seagulls in the first half, although Carole forced him into action with a curling attempt from the edge of the box which the Republic of Ireland keeper held low down.
Albion could have equalised when Leon Knight's quick throw caught the United defence off guard but Jake Robinson hooked wide of the far post.
The same combination almost restored parity in the 36th minute when Robinson, lunging at full stretch to reach Knight's cross, could only direct the ball from whence it came.
Although Albion were in the ascendancy at this stage of the contest United almost punished them from a free-kick by Jagielka, David Unsworth knocking down for Kabba to clip the top of the bar from close range.
Carole is at his most dangerous with the ball at his feet, running at defenders.
The former Monaco winger demonstrated another side to his game early in the second half with a raking pass from defence which threatened to put Knight clean through.
Kenny had to rush to the edge of his area to avert the danger before gathering Jarrett's shot on the follow-up from 20 yards.
Referee Lee Probert incurred the wrath of the Withdean faithful with some strange decisions. He booked five Albion players in an hour and yet allowed Unsworth to escape punishment for a blatant body-check on Carole which was not even penalised with a free-kick.
Albion remained well in the match and United's lead was never comfortable.
Henderson had to save a low shot from Nick Montgomerie to keep the contest alive while a long range free-kick by Richard Carpenter through the defensive wall tested Kenny once more, the visitors' custodian holding on at the second attempt.
There was a bizarre incident in the closing stages, referee Probert consulting his fourth official before having words with Albion's physio Malcolm Stuart.
The equaliser the Seagulls' spirited second half performance warranted should have arrived three minutes from time, Dean Hammond heading the wrong side of the post from Knight's cross.
Frutos, brought on for his compatriot Carole in a flurry of late substitutions by both sides, must now appreciate if he didn't already what English football is all about.
Probert booked nine players in total, even though as Warnock remarked: "I don't think there was a bad tackle."
Albion (4-4-2): Henderson 8; Hart 7, McShane 7, Butters 8, Reid 7; Carole 7, Carpenter 7, Hammond 7, Jarrett 7; Robinson 7, Knight 7. Subs: Oatway, Frutos for Carole (withdrawn 69), Kazim-Richards for Robinson (withdrawn 79), Elphick for Hart (withdrawn 90), Chaigneau.
Sheffield United (4-4-2): Kenny; Kozluk, Bromby, Morgan, Unsworth; Gillespie, Jagielka, Montgomery, Quinn; Shipperley, Kabba. Subs: Ifill for Shipperley (withdrawn 74), Nalis, Tonge for Kabba (withdrawn 90), Armstrong for Quinn (withdrawn 87), Geary.
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