United climbed to fifth in the Premier League following a dramatic night at Bramall Lane.
Oli McBurnie's second-half goal eventually secured three valuable points, but only after a crucial VAR call went in the Blades favour in stoppage-time, as West Ham were denied an equaliser because of a handball by Declan Rice as he challenged John Egan before teeing up Robert Snodgrass.
For the clash against the Hammers, boss Wilder made one change from the side that was beaten at Liverpool, with McBurnie starting in attack, as Mousset dropped to the bench. Also amongst the substitutes was goalkeeper Eastwood, who replaced the injured Verrips.
After a quiet opening five minutes, it was the Blades who forced the first corner of the game following a quickly taken free kick, but Fabianski's punched cleared the danger for the visitors. The Blades continued to force the issue and from another Norwood corner, Egan got a run on his marker, but couldn't direct his header on target.
On 14 minutes, the visitors were forced into an early change in goal, as Fabianski pulled up having taken a goal-kick with what appeared to be a muscular injury and he was replaced by Martin. Haller fired over having got the better of Basham, whilst at the other end Balbuena was ideally placed to block Lundstram's goal bound effort from Fleck's free kick.
As the half hour approached, United suffered a major scare. A long ball forward was misjudged by Egan, but thankfully for the Blades, Anderson dragged his effort wide of Henderson's far post under pressure from Basham. Two minutes of added time were signaled and the half ended with the Hammers on the front foot.
The open moments of the second-half were even, until the Blades had two sights of goal in a matter of seconds. Baldock's cross was only cleared as far as Fleck, his first effort was blocked, but his second, with Martin out of position, went inches wide of the post. Then, from Norwood's short corner and eventually cross McBurnie headed over.
But, from the resulting goal-kick, United took the lead. Martin's pass out was too heavy for Balbuena, Fleck seized the opportunity and squared to MCBURNIE, who slotted the ball under the body of Martin's desperate dive. As the half mark approached, McGoldrick was replaced by Mousset.
United then almost broke to devastating effect following a spell of pressure from the visitors. Stevens played in an advancing Mousset, he squared to Lundstram, who in turn looked for the run of Baldock, but Cresswell made a well-timed tackle to divert the danger away at the expense of a corner.
In 70th minute, from a Snodgrass free-kick, Haller had the ball in the back of the net, the assistant referee flagged for offside though and following a brief VAR check, the decision was confirmed, as Bešić replaced Lundstram in the Blades engine room and in United's next attack, Mousset had a chance to net a second goal, only for Martin to deny him from point blank range after McBurnie had dummied Fleck's through ball.
The game was now an open affair, at one end, Henderson saved well from Lanzini's free kick and was alert to collect the rebound before Haller. The goalkeeper then rolled the ball to Stevens who fed Mousset in down the channel, but the Frenchman blazed over having got the better of Cresswell.
The clocking was ticking in United's favour, but a slip from Egan nearly proved costly, thankfully for the Blades though, Henderson stood tall at his near post to deny Lanzini, before a retreating Egan cleared the danger.
Sharp replaced McBurnie, before Bešić was cautioned attempting to stop the progress of Anderson. From the resulting free kick, Haller headed over at the back post from Snodgrass's delivery.
Three minutes of time were added and it looked like West Ham had snatched a point when Snodgrass beat Henderson at his near post after Rice had got the better of Egan. The players were awaiting the restart following the visitors lengthy celebrations, but referee Oliver stood with his hand to his ear as VAR checked a possible hand ball and the decision eventually went in the Blades favour to the delight of the majority inside the Lane as United returned to winning ways.
Blades: Henderson, Baldock, Stevens, Fleck, O'Connell, Basham, Lundstram (Bešić 70), McBurnie (Sharp 84), Egan, Norwood, McGoldrick (Mousset 59).
Unused: Robinson, Eastwood, Jagielka, Osborn.
West Ham: Fabianski (Martin 14), Zabaleta, Balbuena, Ogbonna, Cresswell, Lanzini (Fornals 84), Noble, Rice, Masuaku (Snodgrass 69), Felipe Anderson, Haller.
Unused: Ngakia, Diop, Gonçalo Cardoso, Costa Da Rosa.
As it happened...
Slow start to this one.
Blades threatened a run down the left but McGoldrick is flagged offside. 0-0.
Lanzini threatening to get in behind Egan who clears, but there's a push in the back of the Irishman and the referee gives a free-kick. 0-0.
Quick free-kick sees Stevens combine with Fleck, the latter's cross is deflected behind for a corner.
Ollie Norwood floats a dangerous cross to the far post but West Ham clear. 0-0.
Teasing low cross from Stevens just archs away from Lundstram who was arriving at the back post.
Follow up cross from Baldock looking for McGoldrick, but West Ham head clear. 0-0.
Chance for United.
Stevens does brilliant down the left to win United a corner. Norwood swings in the corner which is headed over by Egan. 0-0.
We have a stoppage here, Lukasz Fabianski is down, not sure why, but he's going to have to come off...
Replays suggest he's pulled something kicking the ball.
Fabianski is replaced by David Martin.
Long pass from Felipe Anderson picks out Sebastien Haller. The striker puts it through Basham's legs but his effort is high and wide. 0-0.
Chance again for the Blades.
Fleck's free-kick is kept alive by McGoldrick who puts it into a dangerous area. Lundstram is there but his effort is blocked by Balbuena. 0-0.
Game has yet to get going really, nothing much to report as both sides continue to cancel each other out in midfield. 0-0.
West Ham win a corner after a cross deflects behind off Baldock.
The corner is deep, but Basham is there to head clear. 0-0.
Huge chance for the visitors.
Straight ball over the top, and Egan misjudges his header. Anderson beats Basham for pace to run onto the loose ball. He's clean through on goal but drags his shot wide of Henderson's far post. 0-0.
West Ham quickly move from halfway into a shooting position, but Masuaku shoots wide of the near post. 0-0.
A Fleck corner to the far stick is glanced well wide by Lundstram. 0-0.
Wonderful pass from Norwood into the feet of Lundstram who cuts back inside before delivering a deep cross at pace which just eludes the outstretched boot of McBurnie. 0-0.
Two minutes added.
Lanzini corner is comfortably claimed by Henderson. 0-0.
Blades 0 - 0 West Ham
Not much to shout about in this one. Hammers miss the best chance when Anderson shoots wide when through.
Second half is underway
The game livens up as Fleck sees a strong effort blocked. The 'keeper had alread dove to his right, the ball comes back to Fleck at pace but he drills an effort wide of the opposite post. 0-0.
Another chance for United.
Short corner from Norwood gets it back from O'Connell. In goes the cross which is headed over by McBurnie.
Martin passes to Balbuena, there's a mix up. The ball is picked up by Fleck who rounds the defender and finds McBurnie who fires under Martin! 1-0.
Change for United as McGoldrick is replaced by Lys Mousset.
Sweeping counter from United as Stevens weights a perfect pass to Mousset. He sprints to the edge of the area, stops, lays the ball square for Lundstram who has Baldock on the overlap but the pass is slightly too heavy and the wing-back's effort is blocked. 1-0.
Masuaku is replaced by Robert Snodgrass
West Ham have the ball in the net as Haller connects to a Snodgrass free-kick but it is rightly ruled out for offside. 1-0.
Second change for United as Besic is on for Lundstram.
Another dangerous free-kick from Snodgrass causes issues, but McBurnie is fouled and United have a free-kick.
Attendance: 30,124 (2,798)
What a chance and what a move!
Norwood into Fleck, wonderful vision to pass towards McBurnie who dummies allowing Mousset a run on goal but his shot is saved by the feet of Martin. 1-0.
Anderson tripped 25 yards out.
Lanzini hits the free-kick over the wall but it is clawed away by Henderson who also gathers the rebound. 1-0.
Mistake by Egan who slips and allows Lanzini a run in on goal from the angle. Henderson beats away his effort, Egan puts the loose ball behind and from the corner Henderson gathers. 1-0.
Pablo Fornals coming on for West Ham replace Lanzini.
Change for United as McBurnie is replaced by Billy Sharp.
Late challenge by Besic and he's into the book.
Free-kick by Snodgrass is again dangrous and Haller heads down into the ground and over the bar. 1-0.
Three added minutes
Goal for West Ham.
A minute to go and West Ham equalise as Rice avoids several challenges and slides in Snodgrass who nets. 1-1.
No goal!!!! Apparent handball in the build up, we think.
Blades 1 - 0 West Ham
McBurnie's goal wins it for United, as Snodgrass' late equaliser is ruled out by VAR.