Albion were cut down by the promotion-chasing Blades as they suffered their third away defeat on the trot but it was a close shave.
Dean Windass gave United a sixth minute lead only for the Seagulls to respond with a 14th minute equaliser by Richard Carpenter.
Michael Brown clinched the points for the home side with a free-kick from 20 yards on 34 minutes, his 17th of the season.
Bobby Zamora, injured before setting up Carpenter's goal, was eventually forced off early in the second half and Albion also lost midfielders Carpenter and Simon Rodger.
Albion made one enforced change to the team which recorded a fourth home win in a row against Nottingham Forest on Saturday.
A twisted ankle ruled out Anthony Rougier, so Hart returned for his first start for six matches following suspension alongside Zamora.
United also made one change after Saturday's goalless draw at the Seagulls' relegation rivals Stoke.
The influential McCall, back from an ankle injury, resumed in midfield with Jagielka reverting to rightback and Curtis relegated to the bench.
Albion were almost gifted an early goal when a mistake by Page let in Hart. The home captain recovered enough to put Hart off his shot which gave Kenny the most comfortable of saves.
The Seagulls fell behind a minute later. Nobody picked up a diagonal run by Windass inside the area and he latched on to Jagielka's pass to slot his sixth of the season past Beasant from eight yards.
It was a confident finish by Windass, signed for the rest of the season from Middlesbrough, and the worst possible start for Albion against such formidable opposition.
But they have demonstrated time and again that they are made of stern stuff and they were only behind for eight minutes.
Zamora had suffered a knock and was about to be replaced by Barrett when Albion's young talisman produced a sublime piece of skill.
A drag back inside the box took him around the bemused Page and away from the sprawling Kenny before he squared for Carpenter to stroke into the unguarded net from close range.
Zamora signalled to the bench soon afterwards that he wanted to stay on to try and run off the injury.
It was an impressive response by Albion and Sheffield suddenly looked a little shaky. Watson gave Kenny an easy save from a free-kick 20 yards out, then Brooker scuffed his effort to the former Bury custodian following a poor defensive header by Page.
Watson was lectured by referee Fletcher for a foul on Ndlovu. He needed treatment, which gave Zamora the opportunity to jog across the dugout and consult with physio Malcolm Stuart.
The crowd were becoming restless at United's failure to stamp any authority on proceedings after such a promising opening.
The contest turned against Albion again when Cullip was booked for clipping Brown inside the D.
Everyone was expecting Brown to curl the ensuing free-kick over the defensive wall covering the left hand side of the goal.
Instead United's prolific midfielder drilled a low right foot drive beyond the diving Beasant into the opposite corner. It was a clever piece of deception by the highly rated Brown, a target for both Chelsea and Charlton.
Zamora joined Cullip in the book three minutes later following an incident off the ball close to the touchline. Referee Fletcher consulted his linesman before issuing the yellow card to a perplexed Zamora.
The Seagulls suffered a further setback three minutes from the break when the injured Rodger was replaced on the left by Jones.
The Blades made a change for the second half, Curtis coming on for McCall. Curtis went to rightback, with Jagielka returning to the midfield.
Zamora came out for the second period but was replaced within three minutes by Barrett.
Windass dived to head over a corner from Tonge, then at the other end Ingimarsson's header from a Carpenter corner was held by the stretching Kenny.
The pattern of set piece danger continued, Brown producing another expert delivery from a free-kick for Kabba to head wide. It was Kabba's last contribution as he was replaced a couple of minutes later upfront by Peschisolido.
Jagielka picked up Sheffield's first booking for a foul on Ingimarsson, who was now marauding in midfield with Mayo in the centre of defence and Jones wide on the left.
Barrett, no doubt eager to make an impression after his lengthy famine, took the resulting free-kick 25 yards out instead of Carpenter and curled it wastefully over the bar.
Both sides made final substitutions, Albion introducing Oatway for Carpenter in midfield and Morrison replacing Ndlovu for the hosts.
Morrison almost scored immediately, escaping from Blackwell and Cullip before Beasant parried his shot at the expense of a corner.
Windass had his name taken for dissent, which made the caution count 2-2. Albion just wished the scoreline could be the same.
In a stirring finale Barrett had a swerving rightfooter beaten away by Kenny, Oatway was booked for a foul on Brown and Beasant made a fine save to foil Peschisolido.
Beasant and Watson received further bookings in stoppage time as news filtered through of Grimsby's late winner at Rotherham.
- Albion (3-4-1-2): Beasant (gk) 7; Watson (rwb) 7, Mayo (lwb) 7, Cullip (cd) 7, Blackwell (cd) 6, Ingimarsson (cd) 8, Rodger (m) 6, Brooker (m) 7, Carpenter (m) 7, Hart (f) 7, Zamora (f) 7.
- Subs: Jones for Rodger (injured, 42), Barrett for Zamora (injured, 48), Oatway for Carpenter (injured, 67), Wilkinson, Packham.
- Scorers: Carpenter (14).
- Bookings: Cullip (33, foul), Zamora (36, unsporting behaviour), Oatway (80, foul), Beasant (90, unsporting behaviour), Watson (92, foul).
- Sheffield United (4-4-2): Kenny; Jagielka, Kozluk, Murphy, Page, Brown, McCall, Ndlovu, Tonge, Windass, Kabba.
- Subs: Peschisolido for Kabba (withdrawn, 58), Allison, Javary, Morrison for Ndlovu (withdrawn, 69), Curtis for McCall (injured, 46).
- Scorers: Windass (6), Brown (33).
- Bookings: Jagielka (63, foul), Windass (75, unsporting behaviour).
- Half-Time: Sheffield United 2 Albion 1.
- Attendance: 19,357.
- Fan's View: Paul High (Worthing).
I thought we played very well and deserved a point.
I think Bobby going off at the start of the second half seemed to show that we miss him and we don't pose much of a threat without him playing.
The chance Bobby missed just before half time could have changed the match. Their second goal from the free kick was pretty poor defending by us.
With the other results going against us it turned out to be a bad night but if we can carry on playing with this sort of performance I'm sure we can stay up.
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