United recorded a first Premier League away win of the campaign after a 2-0 success over Everton at Goodison Park.
The Blades produced a defensively sound performance aligned with some clinical finishing in attack to stun the hosts - increasing their away points tally to five for the season.
After Yerry Mina put through his own net to hand United the half-time advantage, impressive sub Lys Mousset bagged a superb second to secure a deserved three points for Chris Wilder's side.
Blades manager Wilder made one change to the side with striker Callum Robinson replacing David McGoldrick in attack - the latter missing out with a groin issue.
Everton forced the first half chance on six minutes as Richarlison forced his way through two challenges by Chris Basham before shooting high and wide from a tight angle.
The hosts had another presentable opportunity on 11 minutes when the ball broke kindly for Morgan Schneiderlin lurking on the edge of the area, but he dragged his shot wide via a deflection.
Skipper Ollie Norwood was then cautioned for a late challenge, as the opening 15 minutes passed without major incident.
The home side forced Dean Henderson into his first save on 17 minutes when Lucas Digne took aim from 20 yards, but the Blades stopper parried, and Basham cleared the loose ball.
On 21 minutes both George Baldock and Bernard were cautioned following an altercation as the Blades wing back successfully shepherded the ball behind for a goal kick. Henderson was also shown a yellow for getting involved in the aftermath.
Three minutes later Jack O'Connell ventured forward on the overlap for the first time but his inviting centre rolled all the way across the six-yard area without a touch.
Just before the half hour mark Richarlison aimed an acrobatic effort well wide and Moses Kean smashed a shot well over from 30 yards.
With five minutes remaining until the break United took the lead. After winning a corner down the right, Norwood's delivery was missed by 'keeper Jordan Pickford and the advancing O'Connell only for Toffee's defender YERRY MINA to head into his own net. The Blades faced a nervous wait on the legality of the goal, but following a VAR check, it was rightly given.
United made inroads at the start of the second half when a well worked move found O'Connell advanced, his low centre from inside the area was put behind, and Everton cleared the following corner.
At the other end, John Egan made a brilliant headed clearance from Gylfi Sigurdsson's corner, and as Everton turned the ball back in, Henderson blocked a Kean strike from 12 yards.
Boss Wilder brought on Mousset for Robinson in attack, whilst also made a tactical switch, sacrificing Norwood in place of the grit of Basham in midfield, allowing ex-Toffee Phil Jagielka to slot into the backline.
With 17 minutes remaining, John Fleck broke clear down the left and stood up a cross to the back post where Basham rose but planted his header wide.
United, resolute in defence, then added a second with 12 minutes remaining. The Blades broke from deep with John Lundstram carrying the ball forward before playing a perfectly weighted pass into the path of MOUSSET who timed his run to perfection before sliding the ball underneath the advancing Pickford from a tight angle.
United comfortably held off any potential onslaught from the hosts, as Wilder's side remained rock solid at the back for the remaining 12 minutes, and the four added for injury time.
Everton: Pickford, Keane, Richarlison, Delph, Sigurdsson, Digne, Mina, Schneiderlin (Iwobi 55), Bernard (Tosun 55), Coleman (Walcott 71), Kean.
Unused: Holgate, Calvert-Lewin, Stekelenburg, Davies.
Blades: Henderson, Baldock, Stevens, Fleck, O'Connell, Basham, Lundstram, McBurnie (Osborn 83), Robinson (Mousset 62), Egan, Norwood (Jagielka 63).
Unused: L. Freeman, Morrison, K. Freeman, Moore.
As it happened...
Blades fans in good voice here at Goodison Park as the teams emerge from the tunnel.
Meanwhile, the home fans give a standing ovation to the returning Phil Jagielka, who is amongst the United substitutes.
It was Everton who forced an early corner, but the Blades comfortably dealt with the danger.
Everton forced another corner, before Kean was adjudged to have fouled Basham, much to the annoyance of the home supporters, who expected a free-kick in their favour.
Norwood was booked having caught Delph a few moments earlier.
Henderson called into action to deny Digne, before a combination of Baldock and Robinson relieved the pressure from the resulting corner, with the the latter winning a free-kick on halfway.
Baldock and Bernard were both yellow card following a disagreement on the far side, before referee Hooper booked Henderson for his involvement in the aftermath.
Bernard was looking a live threat on the left and Egan had to be well positioned to halt his progress at the expense of a corner.
GOALLLLLLLLLLLLLLLLLL! United take the lead. Norwood's corner is diverted into his own net by Mina. The goal survived a VAR check for a foul on Pickford, but the Blades lead here at Goodison! (1-0).
Everton almost hit straight back after clever work by Kean on the right, but Henderson saves from Richarlison's header to preserve the lead.
Two minutes of added time is siganlled and a strong tackle from Egan earns him praise from the travelling supporters.
The Blades lead at the break, following Mina's own-goal. An excellent first-half display from United is acknowledged as the players head back to the dressing room.
The second half is underway here at a sunny Goodison, Blades lead 1-0.
Everton's appeals for a penalty are declined by referee Hooper, as Baldock and Bernard came together chasing a deep cross
United looked to make inroads at the beginning of the second-half, but Mina headed clear this time from another flat corner from Norwood.
Double change for the hosts, as Iwobi and Tosun took the places of Bernard and Schneiderlin.
Henderson out smartly to deny Kean, after a couple of corners in quick succession for the hosts.
United's first change saw Mousset replace the hardworking Robinson.
The Blades second change saw Goodison rise as one to welcome on Jagielka, who replaced skipper Norwood, a switch that saw Basham move into midfield.
Everton's final change saw Coleman replaced by Walcott. United still lead 1-0.
United looked to break down the left, but Basham headed Fleck's cross wide, having made up a tremendous amount of ground.
But there was concern for McBurnie, who appeared to have picked up a facial injury.
Bodies on the line from the Blades to deny Everton twice in as many seconds, with O'Connell and then Egan denying Iwobi and Tosun.
GOALLLLLLLLLLLLLLLLLLLLLLLLLLLL! Mousset nutmegs Pickford to double the Blades advantage here at Goodison. Lundstram with an excellent pass, after the Blades had won the ball back on halfway.
Wilder's final change saw Osborn take to the field in place of McBurnie, who received a warm hand from the travelling army of Blades.
Four minutes of added time were signalled and the Blades remained resolute at the back.
GET IN! A first three points on the road comes at Goodison Park, as United deservadly overcome Everton.
A Mina own goal put the Blades in front in the first half, before substitute Mousset adds a second to cap a fine away display, back by tremendous away support as always