John Fleck's second-half double saw United return to winning ways at Bramall Lane.
The Scottish midfielder bagged a well-taken brace, as the Blades produced an excellent second-half showing to net another deserved maximum, with Aston Villa put to the sword.
For the clash against Villa, boss Wilder named an unchanged starting XI following the victory at Norwich City, although there was one change amongst the substitutes with Osborn replacing Robinson, who missed out through illness.
After a quiet opening five minutes, it was United on the attack, with Stevens and O'Connell advancing menacingly, but their crosses into the box were cleared by Hause. Norwood was booked shortly afterwards following three fouls in quick succession, although Grealish and then McGinn on two occasions made the most of it.
Heaton flapped at a Stevens cross, before claiming at the second attempt, before Fleck was cautioned for a soft foul on Guilbert, before the same player was down holding his face after being held off the ball by the stronger Egan.
As half-time approached, goalscoring opportunities remained very much at a premium, although it was the Blades enjoying more possession and territory. Then United had claims for a penalty rebuffed, despite a VAR check, after the ball could have caught the arm of Hause as he blocked Fleck's shot.
Two minutes of added time were signaled, but they passed with incident as the teams went in all square at the break.
The Blades were quickly out of the blocks in the second period, but McGoldrick failed to make contact at the near post, from Norwood's inviting low cross. But on 50 minutes, United deservedly took the lead as FLECK timed his run to perfection and fired home from Lundstram's cross, although it was Basham's backheel that created the opportunity.
In response, Villa broke quickly and registered their first attempt at goal, but Wesley's shot was into the side-netting from El Ghazi's cross. Moments later, Grealish pealed away at the back post and got climbed above Baldock, but thankfully his header went wide of Henderson's post.
Just after the hour, United made a change, with McBurnie replacing Mousset. Hause was booked for a high tackle on McGoldrick and from the resulting free-kick, his header was cleared by Engels with Egan ready to pounce. At the other end, O'Connell was ideally place to clear the danger from Grealish after a fortunate bounce for the visitors, before Targett was carded for a nasty lunge on Norwood.
With 17 minutes remaining, the Blades struck a timely second and what a goal it was too. FLECK started and finished it, this time with his right foot, with Baldock and then McGoldrick heavily involved in the build-up, with the latter claiming the assist with a delightful touch over the defender.
On 76 minutes, VAR reviewed a potential penalty for handball against Egan, the check went in Villa's favour, but from the spot Grealish rattled the bar and despite another stoppage for possible encroachment, referee Bankes waved play on, to the delight of the home faithful.
Bešić took the place of Norwood as the clocked ticked down. Still United poured forward, but McGoldrick fired wide from a low cross by Stevens, before being replaced by Osborn. Five minutes of added time were indicated and they passed with alarm as United recorded back-to-back victories in the top-flight.
Blades: Henderson, Baldock, Stevens, Fleck, O'Connell, Basham, Lundstram, Egan, Norwood (Bešić 86), McGoldrick (Osborn 90) Mousset (McBurnie 61).
Unused: L. Freeman, Sharp, Jagielka, Osborn, Moore.
Villa: Heaton, Guilbert, Engels, Hause, Targett, Lansbury (Luiz 66), Nakamba, McGinn, El Ghazi, Wesley (Kodija 69), Grealish.
Unused: Nyland, Elmohamady, Konsa, Taylor, Trezeguet.
As it happened...
A couple of late tackles going in from Norwood. No cards, but a polite warning from the official. 0-0.
Patient build up down the left involving Fleck.
Ball is played wide to O'Connell who fires in a dangerous low cross aiming for Mousset. Villa clear straight back to O'Connell who crosses again - this time it deflects back off him and goes behind for a goal kick. 0-0.
Norwood into the book. It has been coming, it is his third foul, this time on McGinn, yellow card.
Villa 'keeper Tom Heaton in a spot of trouble after he spills Enda Stevens' cross, but he regains it at the second attempt. 0-0.
Fleck now into the book too for a late challenge on Guilbert.
Game still to get going. United enjoyed a good spell of possession down the right but it ends with a poor cross from Norwood. 0-0.
Villa have Guilbert down, holding his face. We have a VAR check against Egan who held him off. No action taken.
Lundstram feeds Baldock down the right who stands up a cross to the back post. Villa clear but Stevens is running onto the loose ball, he fires over though under pressure. 0-0.
Very little to talk about here. No real chances for either side. 0-0.
Baldock with a deep cross, Stevens attacking the far post heads it into a dagerous area, but Mousset can't get there and Villa clear. 0-0.
We've had a VAR check as Lundstram scuffs an effort goalwards. There are claims for handball against Hause which are quickly waved away. 0-0.
Two minutes added.
Blades 0 - 0 Aston Villa
Not been a thriller this one. United have had more of the half chances but it is 0-0.
The teams are back out here at the Lane.
We're back underway...
Bright start to the second half by United.
Wonderful ball into the near post by Norwood towards McGoldrick who can't make the right connection under pressure. 0-0.
Basham with a lovely backheel to Lundstram who produces a terrific cross which is fired home by Fleck! 1-0!!!!
Counter attack from Villa produces their first effort of the game as Wesley fires into the side netting from a tight angle. 1-0.
Big chance for Villa.
El Ghazi delivers a decent cross from the right to the back post but Grealish heads wide. 1-0.
First change, here comes a sub for United. Oli McBurnie on for Mousset.
McBurnie breaks the offside trap, waits for support, pulls it back but Guilbert somehow deflects the ball over his own bar and Villa clear the corner. 1-0.
Booking for Hause here for a high challenge on McGoldrick.
Engels with an important clearance as United almost profit from a knockdown.1-0.
Change for Villa as Douglas Luiz replaces Lansbury.
Targett booked for a late lunge on Norwood.
Wesley is replaced by Jonathan Kodjia.
Villa benefit from a ricochet in the area as the ball falls to Grealish but from a tight angle and with Henderson advancing he smashes it across the area and United clear. 1-0.
Just when Villa are threatening to get back in the game, United bag a second.
Baldock and McGoldrick are prominent in the build up, with the latter flicking back to Fleck who slots home. 2-0!
We have a penalty here for Villa after a VAR check goes against United. John Egan tried to clear but managed to touch it with his outstretched hand.
He hits the bar!
Henderson dives right and Grealish thunders his shot against the bar!
VAR check about the panalty! It has been waved away, maybe for encroachment?! 2-0 it remains.
McGoldrick from a tight angle sees an effort saved as United go in search of a third. 2-0.
Sub for United as Norwood is replaced by Mo Besic.
Attendance: 30,396 (2,841)
Fleck intercepts and surges forward, at one stage he looked to be through but as he tries to tee up Lundstram the attack ends with a McGoldrick effort which is blocked. 2-0.
McGoldrick sends an effort wide at the near post, it's his last action of the game, as he's serenaded off the field to be replaced by Ben Osborn. 2-0.
Five minutes added
Blades 2 - 0 Aston Villa
Terrific second half from United as a John Fleck brace secures maximum points, with Jack Grealish missing a penalty for the visitors.