A dogged United were the latest victims of unbeaten Liverpool after a 2-0 defeat at Anfield.
The runaway leaders were in top form against the Blades who made Jurgen Klopp's side work hard for their victory after a stubborn display which saw Chris Wilder's side plug away to the end against the World Club Champions.
An early strike from Mo Salah and a second half finish from Sadio Mane was enough to see off the Blades who typically refused to give up.
Wilder made two changes to his side following the recent fixture at Manchester City, with striker David McGoldrick and midfielder John Lundstram retuning to the starting line up in place of Callum Robinson and Mo Besic who were among the substitutes.
Liverpool were forced into a late change as James Milner was quickly rushed into the starting 11 to replace Naby Keita who was originally down on the team sheet.
With the first real attack of the game Liverpool took the lead after just four minutes. Virgil Van Dijk swept a cross-field pass out to the left where George Baldock slipped at the crucial moment allowing Andy Robertson to send in a low cross for Salah to convert from close range.
United almost replied instantly when the returning Lundstram was quickest to a second ball following a defensive header, but his looping effort from just inside the area fell just wide of the far post.
Soon after and Alisson was tested when he was forced to tip over a rasping effort from McGoldrick from the edge of the area.
On 11 minutes United had Dean Henderson to thank for avoiding a second goal after Jordan Henderson's low cross was turned towards the top corner by Salah, only for the Blades' number one to spring to his left to tip the ball over.
The Blades had the ball in the net on 14 minutes when Lundstram sprinted onto a Baldock pass and slid the ball beyond Alisson, but the flag had long since been raised for offside - a decision upheld following a VAR check.
The hosts created another opportunity on 18 minutes when Mane burst down the left before sliding a pass into Gini Wijnaldum who curled an effort past Henderson's far post.
On the half hour mark Henderson was alert again when a straight ball was flicked into the path of Salah by Mane. The Egyptian took aim and powered a shot towards goal, but Henderson got both hands to it to push the ball away.
The hosts lived up to their pre-match billing as they dominated possession but United stuck to the task and almost had a chance to level just before the break, but Fleck's pass to free Lys Mousset was intercepted by Van Dijk.
United quietened the home side at the start of the second half, but on 56 minutes the lively Roberto Firmino cut in from the left before unleashing a fierce drive from the angle which flashed just wide of the far post.
On the hour mark United had a let off when Salah's innocuous looking dinked cross from the edge of the area was missed by everyone, but the Blades were relieved to see the ball bounce off the inside of the post into the arms of Henderson.
The resistance though was broken on 64 minutes. The move started with Alisson as Liverpool worked their way up the left through Mane who played a near one-two with Salah. His first effort was brilliantly kept out by Henderson, but the stopper was helpless as Mane gobbled up the rebound to make it 2-0.
The Blades made a double change with Billy Sharp and Oli McBurnie replacing Mousset and McGoldrick.
Henderson was called into action again on 69 minutes as Trent Alexander-Arnold's low cross was scrambled clear by the Blades only as far as Salah, whose low effort was turned around the post by Henderson.
The home side looked hungry for more goals and Mane again tested the reflexes of Henderson who was equal to his powerful effort thundered in from a tight angle.
United almost pulled one back with three minutes remaining when Jack O'Connell's whipped centre picked out McBurnie at full stretch, but his connection saw the ball divert into the hands of Alisson.
Liverpool: Alisson, Alexander-Arnold, Gomez, Van Dijk, Robertson (Lallana 88'), Henderson, Wijnaldum, Milner, Mane (Origi 77'), Salah (Elliott 90'), Firmino.
Unused: Adrian, Phillips, Jones, Williams.
Blades: Henderson, Baldock, Stevens, Fleck, O'Connell, Basham, Lundstram, Egan, Norwood (Besic 77'), McGoldrick (Sharp 64'), Mousset (McBurnie 64').
Unused: Robinson, Jagielka, Verrips, Osborn.
As it happened...
Referee Tierney blows the first whistle, we're off and running.
Goal for Liverpool. van Dijk's long ball forward finds Robertson and Salah slids home under Henderson from close-range.
United's response is almost instant, Lundstram's looping volley has Alisson stranded but the ball drops inches wide of the far post.
It's the Blades on the attack again, with McGoldrick firing an effort at goal after a header from Norwood, that forces Alisson to tip over.
From the resulting short corner though, United are caught offside.
Only an excellent save from Henderson keeps the score at 1-0. From Jordan Henderson's low cross, Salah diverts the ball goal, but United's number one somehow claws it out of the top corner.
United have the ball in the net with Lundstram firing past Alisson, despite the assistant referee flagging for offside.
The goal is checked by VAR and subsequently ruled out.
Liverpool break at pack with Mane instrumental, but thankfully Wijnaldum's effort from the edge of the box sails high and wide.
Liverpool break at pace again, Mane's dummy frees Salah, but Henderson is equally to his shot.
The hosts then force three corners in quick succession but United hold out.
Half-time approaching here at Anfield.
Liverpool still lead 1-0.
One minute of added time is signalled.
Half-time here at Anfield, the hosts lead 1-0, courtesy of Salah's early goal
The action is back underway here at Anfield.
United looking for a way back into the game against the European champions here at Anfield, had a couple of promising attacks since the restart.
Liverpool, after a long spell of possession come close to scoring a second, but Firmino's curling effort from the corner of the penalty area goes wide of Henderson's far post
United have another let off, Salah's dink into the box evades everyone, but thankfully the ball falls into the hands of Henderson off the far post.
Goal for Liverpool. The home side break at pace once again, Mane combines with Salah and despite Henderson's best efforts, scores at the second attempt.
Double change for the Blades, with McBurnie and Sharp replacing McGoldrick and Mousset.
The hosts, kicking towards the Kop end, go looking for a third, but Henderson is equal to Salah's shot, after Firmino failed to convert from a low cross from the right.
A save from Henderson is required to deny Mane from a tight angle.
Sub for the hosts, as Origi replaces Mane.
United's final change sees Besic introduced, replacing Norwood.
United force a couple of corners, in quick succession, but O'Connell is penalised for a foul.
United's best chance of the night falls to McBurnie at the far post from O'Connell's flashing cross across the face of goal, but the Scottish international can't get enough the ball to beat Alisson.
Lallana takes the place of Robertson.
Two minutes of added time to play at Anfield.
Salah is replaced by youngester Elliott.
It's finished here at Anfield. Liverpool run out 2-0 winners, despite a dogged performance from the Blades.
One that is acknowledged by the travelling fans as the players head over to thank them for their continued support.