United slipped to a first home league defeat since January, as Richarlison's goal proved the difference between the two sides on Thursday evening.
The Blades enjoyed good spells in a tightly fought, but the Brazilian's header early in the second period settled the contest in Everton's favour.
Boss Wilder named an unchanged starting XI for the clash against the Toffees, despite last Thursday's loss at Leicester City. There was one change on the bench though, with Clarke replacing Mousset.
After a quiet opening, it was United who forced the first corner of the contest, but in the second phase, Pickford claimed Osborn's cross comfortably. In United's next attack, Pickford could only palm behind Norwood's free-kick and from the resulting corner from the left O'Connell was inches away from connecting at the back post.
Everton's first foray forward saw Sigurdsson get Walcott in behind O'Connell, but Henderson saved that effort with his feet from a tight angle, before United eventually cleared their lines. Calvert-Lewin then threatened, but poor control from a Gomes pass allowed Henderson to snuff out the danger.
The half hour mark ticked by and United forced another corner, but Calvert-Lewin headed clear and on the break, Osborn was forced to halt Walcott's progress, before Davies was booked for a needless nasty lunge on McBurnie in the middle of the park. Goalscoring opportunities were at a premium, but Basham forced Pickford to take action having advanced forward into a promising position.
With half-time approaching United suffered a real scare. Henderson could only punch Sigurdsson's corner to Walcott and from his deep cross Calvert-Lewin headed against the far post. Norwood was then harshly cautioned despite winning the ball fairly in a challenge with Richarlison moments before referee Attwell blew for the interval.
Within a minute of the restart though, United fell behind from a set-piece. Sigurdsson delivered and RICHARLISON got across the front of his marker and glanced a header past the dive of Henderson. Moments laters Everton broke, with Gomes freeing Walcott, thankfully though a combination of Egan and Henderson averted the potential danger.
On 55 minutes, United were almost handed a way back into the game, Baldock and Basham combined on the right and Keane couldn't clear a low cross from the latter, unfortunately for the Blades though Pickford reacted quickest. At the other end, Calvert-Lewin got the better of Egan, but Henderson managed to claw away his deflected effort.
United made a double change on the hour with Sharp and Fleck replacing McBurnie and Osborn. And then Lundstram took the place of Norwood, with Berge dropping into a deeper role. After Digne had headed behind for a corner, Pickford flapped at Fleck's inswinging delivery, but the referee awarded a free-kick.
The Blades were starting to force the issue as the clock ticked down, although the visitors managed to disrupt the tempo with a number of fouls, with Calvert-Lewin booked for a forearm to the head of Stevens.
Seven minutes remained when Živković was introduced, moments after Gomes had come close from distance. The late substitute was getting down the side of Everton's back line, but from a Stevens cross, Baldock couldn't keep his header down.
Four minutes of added time were signed by the fourth official, but try as they might, the Blades just couldn't find a way to breakthrough the Everton defence down, as a run of four consecutive home league victories came to a disappointing end.
Blades: Henderson, Baldock (Živković 83), Stevens, O'Connell, Basham, McBurnie (Sharp 60), Egan, Norwood (Lundstram 69), McGoldrick, Osborn (Fleck 60), Berge.
Unused: Jagielka, K. Freeman, Robinson, Clarke, Moore.
Everton: Pickford, Digne, Keane, Branthwaite, Sidibe, Sigurdsson (Coleman 88), Davies, Gomes, Walcott (Gordon84), Richarlison, Calvert-Lewin.
Unused: Stekelenburg, Virginia, Baines, Iwobi, Bernard, Baningime, Simms.
As it happened...
It's United to kick-off and we're underway...
Nothing to report so far other than a couple of free-kicks to the away side. 0-0.
Through ball looking for Walcott who is a mile offside but there's an anxious wait before finally the flag is correctly raised.
United force a corner down the right.
Norwood delivers looking for Egan, but Michael Keane rises to head clear.
Everton trying to play out from deep without any success.
Berge wins it before being fouled. Norwood takes the free-kick deep and Pickford claws behind for a corner.
Norwood with a wicked delivery which looked as though it might go in after Pickford gets nowhere near it, but it goes just wide with O'Connell also close to connecting.
First sign of intent from Everton.
Walcott found in the right channel of the United area, but there's no takers as he lays a dangerous low centre across the six-yard box.
Counter attack from Everton.
Andre Gomes breaks down the right and opts to cross early. Calvert-Lewin takes it on the run, but the touch off the chest is heavy and the ball runs through to Henderson.
Break in play as Richarlison goes under holding his head under a challenge by Berge.
He's back on after treatment. 0-0.
Digne with a challenge on Basham, the ball goes behind for a corner.
Norwood's cross, this time to the near post, headed clear by Calvert-Lewin.
First yellow of the game goes to Tom Davies for upending Oli McBurnie.
Crucial header behind by Digne as Baldock almost got onto Norwood's ball into the channel.
Norwood's corner is to the near post again, headed clear to Stevens 25 yards out but he fires well over.
Norwood with another United corner, headed up in the air at the back post by McBurnie, and claimed by Pickford.
Everton playing their way into trouble again after losing the ball playing out.
Basham crosses down the right, Pickford gets a hand to it and it runs clear.
Everton corner after Richarlison plays the ball off Baldock.
Sigurdsson's corner punched clear by Henderson. Walcott returns it to the back stick where Calvert-Lewin plants a header against the post.
Two added minutes.
Norwood picks up a yellow after a challenge on Richarlison.
Blades 0 - 0 Everton
Level at the Lane with United enjoying plenty of the ball, but Everton hit a post through Calvert-Lewin.
Teams back out here for the second-half.
Everton get the second-half underway.
Came from nowhere. Free-kick midway through the Blades half. Delivered into the near post by Sigurdsson and flicked into the far corner by Richarlison.
Good response by United. A cross from the right brought down by Stevens but as he goes to strike the ball, he's blocked by two in blue.
United again on the front foot, Baldock finds Basham who cuts the ball back from the by-line but McGoldrick rifles his shot against an Everton defender.
Luck for Everton who don't defend a low Basham cross well at all.
It hit the back heel of Keane who turned away at the same time. It could have gone anywhere, but Pickford was alert and dived on the loose ball.
Chance for the visitors.
Calvert-Lewin wrestles clear of Egan, drives into the area, but his deflected effort is saved by Henderson.
First change for United as Billy Sharp replaces Ben Osborn.
It's a double change, with McBurnie being replaced by John Fleck.
Danger for United as Walcott makes progress down the right, but his cut back slices through several bodies and United clear.
Chances at a premium so far, big 25 minutes now.
Substitution for United as Norwood is replaced by John Lundstram.
Deep cross to the back post and Digne has to head behind.
Fleck delivers the corner, Pickford comes and loses the ball but the officials say there's a foul by Sharp. Free-kick to Everton.
Baldock almost in behind, sliding challenge by Davies, wins the ball - corner to United.
Fleck delivers but Calvert-Lewin flicks the ball clear.
Fleck with a lovely pass through the gap for Sharp who couldn't quite collect otherwise he would have been potentially in on goal.
Calvert-Lewin booked for a late challenge on Stevens.
Half-a-chance for Everton as Walcott slides a ball through the six-yard box but no touch from Richarlison or Calvert-Lewin.
Long-range strike from Andre Gomes whistles just wide.
Basham is replaced by Richairo Zivkovic.
Everton change. Walcott is replaced by Anthony Gordon.
United coming forward in numbers.
Stevens is found inside the area, he gets the ball out of his feet and crosses but Baldock heads over.
Another change for Everton. Seamus Coleman replaces Sigurdsson.
Richarlison is booked for stopping the restart.
Four minutes added time.
Stevens is freed in the channel, the cross comes in, Egan rises but he can't get a clean connection and Everton clear for the time being.
Everton break and Gordon gets into a shooting position but decides to cross - no-one there though and United clear.
Blades 0 - 1 Everton
Richarlison's second-half header is the difference as the Blades are beaten.