The visitors, who are still without a win this season, had played for 55 minutes with ten men after John Lundstram was sent off for a foul on Joel Veltman, but they went in front through Jayden Bogle early in the second half.
The Seagulls bossed possession, but the Blades were well organised and looked to be on their way to their first win of the Premier League season but only before Welbeck pounced from close range four minutes from time.
Albion began on the front foot with Leandro Trossard and Solly March prominent, although it wasn’t until midway through the first half before United keeper Aaron Ramsdale was tested when he saved an angled effort from Aaron Connolly, who had been played in by a through ball from Adam Lallana.
Graham Potter’s men then had two great chances in the space of six minutes. Yves Bissouma released Trossard down the right, who in turn picked out Neal Maupay but his effort was blocked by Chris Basham and fell into the grasp of Ramsdale.
The French striker was involved again after the half hour mark when Adam Webster met Trossard’s corner that Maupay turned goalwards, but Ethan Ampadu got the block in to deflect it away.
Robert Sanchez had been a spectator in goal on his home debut, but the Spaniard made a great save to deny David McGoldrick, who fired a free-kick from the edge of the D towards the bottom corner.
The visitors grew into the game, but were dealt a hit when they went down to ten men in the 38th minute. Referee Peter Bankes initially showed Lundstram a yellow card for a challenge on Veltman, but after VAR intervention he changed his decision and gave the Sheffield United #7 his marching orders.
Potter made an attacking change at the break, bringing on Ali Jahanbakhsh and with only Oliver Burke on his own up front, United set their stall out to stay compact and make it difficult to be broken down.
As a result, Albion dominated possession but were nearly punished when Burke broke from halfway and laid the ball into the path of Enda Stevens, but he drilled his effort just wide of the post from 18 yards.
The Seagulls looked low on attacking ideas, and things took a turn for the worst after the hour. The tireless McGoldrick picked out substitute Bogle and his strike from just inside the box deflected off Webster and flew into the roof of the net.
Webster then nearly made a decisive intervention at the other end when his shot was palmed over by Ramsdale, but as the time wore on the hosts were getting more and more frustrated in front of 2,000 fans on the south coast.
The arrival of Andi Zeqiri, for his Albion debut, and Welbeck from the bench provided different attacking threats, but with 15 minutes to go the Blades were looking comfortable.
Lewis Dunk could only head March’s corner straight at Ramsdale, before Connolly looked set to score with eight minutes to go, after the keeper missed Jahanbakhsh’s cross, but he could only head over from inside six yards.
Burke nearly doubled the visitors’ lead on the counter, firing wide from George Baldock’s cross before Albion finally broke through. Basham and Webster went up to compete as Trossard whipped the ball in and it fell to Welbeck, who chested it down in a crowded six yard box and volleyed it past Ramsdale.
There was still time for further drama as the hosts looked to win the game. Welbeck saw an effort blocked on the line and the loose ball fell to Jahanbakhsh, but he could only head the ball against the bar from point blank range to sum up a frustrating afternoon for the hosts.