John Egan was United's hero as his late header secured three crucial points against Wolves at a soaked Bramall Lane.
The Blades more than held their own against Nuno Espírito Santo's side and having forced their opponents back in the second-half Egan headed home Norwood's corner in the last minute of added time to make it goals in consecutive games for the defender and back-to-back home victories for United.
For the clash against Wolves, boss Wilder made two changes, with O'Connell handed his first start since the resumption in place of Robinson and Sharp replacing the injured McGoldrick in attack.
It was a positive start from the Blades, who enjoyed plenty of the ball and pushed the visitors back, although there was little in the way of goalmouth action the opening ten minutes or so. Both sides were struggling to make the final pass a telling one, with Egan having to be alert to some potential danger from Jota's low cross after a slip by Osborn.
On 18 minutes, United registered a first attempt on goal but at the near post, Rui Patrício was equal to McBurnie's header from O'Connell's centre. As the half hour approached, Wolves responded with a headed effort of their own, but Henderson wasn't troubled by Jota's looping attempt.
But moments later there was real concern for United as Wolves broke at pace. Jota combined with Jimenez and advanced towards goal where O'Connell unfairly halted his progress at the cost of a booking and from the resulting free-kick, Neves struck the crossbar from 20 yards out. With half-time approaching United finished on the front foot, with successive corners, but unfortunately Jimenez cleared the first and Doherty the second as it remained goalless at the break.
In the opening minutes of the second period, Wilder made his first change with Mousset replacing McBurnie, but like the first, goalscoring opportunities were very much at a premium. On 53 minutes though, United had the ball in the net, with Sharp firing home with the aid of a deflection, only for the assistant referee to intervene and his decision was confirmed by VAR.
The hour mark was insight when the Blades produced the best move of the game to so far, which saw Sharp inches away from converting Stevens cross after the home side had passed the ball forward from back to front, drawing Wolves in. In response, the visitors threatened as Traore broke at pace, Stevens would be for a late challenge, but referee Atkinson allowed play to continue with Jota heading over a Jimenez cross.
The drinks break saw United make a second change with Živković introduced in attack, replacing Sharp. Again, United built from the back and Živković found time and space on the edge of the box, but despite getting a run on his marker, Baldock couldn't keep direct his header on target.
The clocking was ticking, but it was United who remained positive, as more excellent play yielded a corner, but Jonny was positioned well to clear O'Connell's cross in the second phase. Three minutes of added time were signalled and Doherty's handball gave United a big chance late on which almost caught Wolves napping.
But following some sustained pressure at the death, the Blades eventually netted a deserved winner. Norwood's corner from the right was inviting and EGAN rose highest in a crowded penalty area to head past Rui Patrício as Wilder embarked on his trademark celebration run towards the Kop end.
Blades: Henderson, Baldock, Stevens, O'Connell, Basham, McBurnie (Mousset 49), Sharp (Živković 71), Egan, Norwood, Osborn, Berge.
Unused: Lundstram, Jagielka, K. Freeman, Robinson, Moore, Rodwell.
Wolves: Rui Patrício, Boly, Coady, Saïss, Doherty, Rúben Neves, João Moutinho, Jonny, Traoré (Dendoncker 79), Jiménez, Diogo Jota.
Unused: Ruddy, Jordad, Podence, Gibbs-White, Vinagre, Campana, Kilman, Buur.
As it happened...
Wolves kick-off and we're underway...
Early stoppage as Wolves' Traore is down holding his shoulder after a nudge by Stevens.
After treatment he's back up, and we're underway again.
Steady start by both teams. Nothing really to report as yet.
Stevens threatened at the by-line but his low cross is blocked. Osborn's follow up is also cleared. 0-0.
Searching ball forward looking for the dangerous Jimenez. Just too strong on this occasion as Henderson scampers off his line to collect.
Good start again by United as Wolves are forced to defend a dangerous Norwood centre.
Norwood threads a pass through towards Sharp who thought he'd broke the Wolves line, but the flag is raised and the skipper is adjudged to be just offside.
First real sign of danger from the visitors. A long ball forward is aimed at Jimenez in an offside position, but he moves away from the ball and the onside Traore picks it up, and drives into the area.
His cross hits Jimenez, and the ball runs away from him allowing United to clear.
Wonderfully weighted pass from Berge into the right channel. Baldock crosses low into the area and a clearance hits another Wolves body but it is a fortunate deflection for the visitors who eventually clear.
O'Connell whips a lovely cross into the area which is met by the head of McBurnie but Patricio is well placed to hold.
Danger as Traore takes on Stevens and drives a low into the area. This time there's no-one in gold close enough to attack the cross and United clear.
United have looked good at times in the opening quarter, but Wolves do have a threat with Traore down the right.
Ball worked across field by Wolves out to the dangerous Traore. He heads for the by-line before digging outa cross towards the far stick where Diogo Jota wins a header but Henderson is there to claim.
Yellow for O'Connell as he pulls down Jota with Wolves counter attacking.
Free-kick in a dangerous position.
Neves takes aim, over the wall, beats Henderson, but it hits the bar and goes over.
Good spell for Wolves as Jimenez bursts down the right of the area, he clips in a cross but Henderson anticipates well to make a claim at the near post.
Neves with another long range strike after some patient Wolves build up. It flashes over with Henderson comfortable.
Stevens with a perfect pass for Sharp and this time he beats the offside trap. He cuts the ball back from the by-line but Wolves clear behind. Or so we thought as the ref gives a goal kick.
Chance for United!
Poor pass by Doherty and Sharp is in on the angle, but out comes Patricio and saves with his legs .
Henderson well positioned again as Neves fires in another low cross from the by-line. Gathered comfortably by the United stopper.
Wonderful cross from Stevens after he's picked out on the left by Osborn.
A vital Wolves clearance with several in red and white waiting to pounce.
Three added minutes
Two Norwood corners cleared by Wolves as United finish the half strongly.
Low Doherty cross to the edge of the area is smashed well wide first time by Moutinho.
Blades 0 - 0 Wolves
Sharp closest for United but it is a tight encounter, all to play for in the second half.
Blades back out for the second half...
Blades get the second half underway.
Lys Mousset preparing to come on shortly for United.
Meanwhile, Basham on the overlap bursts down the right and crosses into the hands of Patricio.
Here comes the first change.
Oli McBurnie is off and Mousset is on.
United head clear a Wolves free-kick after Jimenez was fouled. The ball runs for Neves who never turns down a chance to shoot, this time he hammers the ball over. Goal kick.
Ball in the net for United but the flag is up.
Stevens with a wonder pass into Sharp who turns and fires into the net, but the Wolves defence stepped out and the flag rightly goes up for offside.
Another inviting cross from Stevens - not for the first time tonight.
Both Mousset and Sharp fling themselves forward but can't quite get there and Wolves escape.
Wolves have been quiet this half but all of a sudden they burst forward on the counter through Traore.
Stevens tries to halt his break but can only delay him, the ball goes right as Jimenez crosses for Jota but he gets his header all wrong and wastes the chance.
After that Wolves attack, the referee shows the yellow card to Stevens who tried to stop the attack.
Half a penalty appeal as Basham challenges with Jimenez but the referee is well placed and isn't having any of it.
Sub for United as Zivkovic replaces Sharp.
Zivkovic bundled over on the far side, just outside the area.
Norwood delivers the free-kick low into the near post and Jimenez beats Zivkovic to ball to clear for Wolves.
Chance for United.
Zivkovic the provider with a deep cross to the far post and Baldock made it his, headed down but just wide of the far stick.
Wolves making a change as Traore is replaced by Leander Dendoncker.
United counter sees Mousset sprint forward deep into the Wolves half, but his shot from distance is wild and wide.
United looking the more likely here as Basham raids down the right earning a corner from his low cross.
Wolves stand firm to Norwood's testing delivery.
Wolves looking tired now and certainly look happy with a point.
United still pressing for a winning goal.
Three added minutes.
Blades free-kick after a handball.
It's clever, Berge to a breaking Osborn but the low cross is cleared by a raft of diving gold shirts.
Cross into the area causes panic and pinball and a deflected Osborn shot goes wide.
United snatch it at the death.
Norwood's corner is powered in by Egan!!
Blades 1 - 0 Wolves
Egan's last gasp header gives United the three points.