United made it three wins on the spin, and stayed unbeaten on the road in the Premier League, after a 1-0 success at Brighton and Hove Albion.
Oli McBurnie's well-taken first-half strike, his third of the season, was enough to send the Blades supporters home for Christmas in high spirits, and it could have been more as United had two goals disallowed by VAR.
Boss Chris Wilder made two changes to the side which beat Aston Villa last time out.
With John Fleck serving a suspension he was replaced in the side by Luke Freeman, whilst McBurnie, impressive in training, was recalled with Lys Mousset on the bench.
Callum Robinson also returned to the bench after illness, whilst Michael Verrips replaced Simon Moore who had tweaked a groin.
Wilder's side looked to have made an early breakthrough on a first visit to the Amex when Luke Freeman's corner was missed by Brighton 'keeper Mat Ryan, allowing John Egan to bundle the ball into the unguarded net. Following a VAR check the goal was chalked off after it was adjudged to have gone in off the Irishman's hand.
On 16 minutes United worked another opening. John Lundstram pinched the ball just outside the Albion area, he played a one-two with George Baldock, but rattled an effort into the side netting.
Brighton threatened when Aaron Mooy's effort was saved by Dean Henderson. Martin Montoya picked up the loose ball and squared for Neal Maupay to net, but the flag was rightly raised for offside.
The Blades continued to carry a threat and opened the scoring on 23 minutes. Henderson's booming clearance caused panic in the Brighton defence, and after a poor header by Adam Webster, McBURNIE sprinted clear to coolly slot beyond Ryan under pressure.
Shortly after a perfectly weighted David McGoldrick pass almost had Lundstram through but he couldn't get his shot away under pressure.
The Blades were creating the better openings and were dominating the half, but Maupay still carried a threat as he glanced a header well wide from a right-wing cross.
At the other end Jack O'Connell planted a header from Ollie Norwood's corner wide, but the referee had also blown for a push on a Brighton defender.
Brighton boss Graham Potter acted at half-time making two changes as Glenn Murray and Aaron Connolly replaced Leonardo Trossard and Pascal Gross.
United were inches away from making it 2-0 on 49 minutes. Another long ball forward caused alarm for Webster as McGoldrick muscled him off the ball before carrying it forward, rounding the 'keeper but from a tight angle his low shot hit the outside of the post.
Wilder then made a change as Ben Osborn replaced Luke Freeman on 53 minutes.
The Blades netted again shortly after but once again VAR came to Brighton's rescue. Norwood's free-kick was headed towards goal by Egan, Ryan spilled it straight to O'Connell who netted but the video referee disallowed the strike for offside.
Brighton then made their final change as Yves Bissouma replaced Montoya, whilst the Blades brought on Mousset for McBurnie.
The Blades had the better of the opening 15 minutes of the half, but the home side started to come back into the contest as two Mooy crosses forced the United backline into some scrambling defence.
Norwood came to United's rescue when he made a fantastic block after Davy Propper lined up a shot from 25 yards, and soon after Henderson tipped over a Connolly effort from 20 yards.
On 75 minutes Enda Stevens became the first name into the book after stopping a counter with a trip.
Egan made a great interception to halt a Brighton move down the right and also headed clear the resulting corner as United stayed strong at the back.
At the other end the Blades came within a whisker of a second as Mousset cut in from the left, beat two players, but fired an effort just over from 20 yards. Whilst a few minutes later, McGoldrick steered Osborn's cross over the bar on the stretch.
Late bookings for Basham and McGoldrick were handed out, but United saw out the final moments to record yet another away win.
Brighton: Ryan, Montoya (Bissouma 55), Dunk, Webster, Burn, Stephens, Propper, Mooy, Gross (Connolly HT), Trossard (Murray HT), Maupay.
Unused: Button, Alzate, Duffy, Bernardo
Blades: Henderson, Baldock, Stevens, O'Connell, Basham, Lundstram, L. Freeman (Osborn 53), McBurnie (Mousset 63), Egan, Norwood (Besic 82), McGoldrick.
Unused: Sharp, Robinson, Jagielka, Verrips.
As it happened...
We are underway...
Blades in a third strip of yellow for the first time this season.
Dangerous early cross into the near post towards McGoldrick, but Brighton defend well as United make a good start.
Baldock breaks to the by-line and wins a corner for United.
First attempt by Freeman ends up going behind for another corner. His second attempt is missed by Ryan and Egan bundles the ball in! 1-0 Blades.
Hang on VAR check...
Disallowed! It's 0-0. Egan adjudged to have handled.
Quiet spell since the Blades goal was chalked off. 0-0.
Lundstram pinches the ball back for United just outside the Brighton area. He plays a one-two with Baldock before unleashing a shot into the side netting. 0-0.
Brighton thought they'd gone in front when Mooy's shot was parried by Henderson to Montoya, who cut the ball back for Maupay to net, but the flag was rightly raised for offside. 0-0.
Dunk hammers a free-kick well over from 25 yards after a foul by Lundstram. 0-0.
It's McBurnie for the Blades and this time it stands! Huge clearance by Henderson, a mistake at the back by Brighton and McBurnie coolly slots the ball beyond Ryan. 1-0 Blades.
McGoldrick with a wonderfully weighted pass for Lundstram who is almost in but the ball wouldn't quite run right to shoot and Brighton clear. 1-0 United.
Dunk with a run forward from the back but his low cross is claimed by Henderson.
Soon after Maupay glances a header well wide. 1-0 Blades.
Henderson has to be quick off his line to clear as Brighton send a ball in behind the full back position. 1-0 Blades.
Here comes the rain!!!
Quick thinking by O'Connell from a throw wins United a corner.
Norwood's corner finds the head of O'Connell at the back post, but he plants his header wide. The referee also blows for a push by the Blades defender.
One added minute
Brighton 0 - 1 Blades
McBurnie's strike is the difference at the break, as Egan also has a goal disallowed by VAR.
We are underway again...
Two changes for Brighton at the break as Murray and Connolly replace Trossard and Gross.
So close to a second!
Long ball over the top and McGoldrick has done brilliant to force the mistake from Webster, take it on, round the keeper, but his shot from a tight angle hits the outside of the post.
Change for United as Ben Osborn replaces Luke Freeman
Blades denied a second goal by VAR when Egan's header from Norwood's free-kick is fumbled by the 'keeper and put in by O'Connell, but he is offside. No goal.
Change for Brighton as Yves Bissouma replaces Montoya.
Dangerous Mooy corner headed clear by O'Connell as Brighton enjoy their best spell of the game.
Lys Mousset replaces McBurnie.
Two dangerous Mooy crosses give United's defence something to think about as Brighton fail to take a couple of half chances.
Propper lines one up from the edge of the area but Norwood makes a terrific block.
Shortly afterwards Connolly's effort from 20 yards is tipped over by Henderson and nothing comes from the corner.
Stevens is in the book for a trip.
Egan makes a great interception from a low cross as Brighton attack down the right.
The same player then heads clear the resulting corner.
Fantastic run from Mousset as he cuts in from the left and beats two players but he fires an effort from 20 yards just over.
Final change for United as Mo Besic replaces Norwood.
Basham booked for a trip on the right edge of the area.
Chance for United on the counter as Osborn clips a cross to the back post but McGoldrick on the stretch puts it over.
McGoldrick sees yellow for stopping a counter
Bissouma yellowed for simulation as he attempts to win a penalty.
Five added minutes
Murray rises to try and meet a cross into the area, but he is penalised and it is free-kick to United.
Mooy cross is headed over by Webster.
Brighton 0 - 1 Blades
McBurnie's first half goal wins it for United who have two goals taken off by VAR.