United battled valiantly, but slipped to defeat against Liverpool at Bramall Lane on Sunday evening.
Second-half goals from Curtis Jones and Roberto Firmino were enough for the visitors in a game where United did have chances against Jurgen Klopp's Reds.
Boss Wilder made two changes for the hosting of the Premier League champions. Norwood and McGoldrick returned to the starting XI, with the latter captaining the side, as Sharp dropped to the bench.
The first five minutes saw both sides struggling for controlled possession. But United won a free-kick in a promising as Phillips fouled McGoldrick. Norwood's delivery was inviting, but Adrian saved from the stand-in skipper before Alexander-Arnold hacked clear. But in the 11th minute, only an excellent save from Ramsdale kept the game goalless. Mane challenged Ampadu and the ball fell kindly for the onrushing Firmino, but United's number stood tall and denied him, before clawing out Robertson's cross from underneath the crossbar.
The game was open and Adrian was called into action for a second time after McBurnie controlled before McGoldrick's placed effort was deflected which caused the experienced stopper a moment of concern. Liverpool responded and a quickly taken throw-in on the right created space for Alexander-Arnold to cross to the back post, Jones got in front of Baldock but Ramsdale smothered the danger.
As the half mark approached, Liverpool sprung forward again, Firmino helped the ball on to Salah, he got the better of Jagielka, but again Ramsdale was there to save. Ampadu then surrendered position in his own area, Alexander-Arnold latched on to it, got past Stevens, only for Ramsdale to tip over at the expense of a corner that came to nothing.
The Blades had the ball in the net nine minutes before the break after McBurnie competed with a Kabak who managed to wrong foot Adrian, unfortunately though VAR intervened and McBurnie was adjudged to have been offside. At the other end, Ramsdale continued to deny the visitors, this time saving from Wijnaldum before Firmino squared the rebound and Ampadu cleared and that was the last action of the first period.
Liverpool took the lead on 49 minutes, although United can feel aggrieved as the ball appeared to be out of play on the byline before Alexander-Arnold cut back for JONES to fire past Ramsdale. Four minutes later, the visitors had the ball in the net again, but this time VAR correctly ruled in United's favour as Mane was in an offside position as Robertson prodded forward.
The Blades responded with a double change, as Osborn and Burke entered the fray, prompting a change of formation in the process, as Jagielka and McGoldrick were withdrawn and within moments of the change, Norwood's cross to the near post was inviting, but McBurnie headed wide. The Scottish international then got in behind, but his touch allowed Kabak to clear, from the resulting corner, Adrian punched to the edge of the area but Norwood's low effort went wide.
And those missed opportunities to restore parity were punished at the other end on 65 minutes. FIRMINO advanced past two or three challenges before getting a fortunate deflection that cruelly wrongfooted Ramsdale. United were enjoying more possession and territory as Liverpool dropped deeper, but on the break it was Robertson who fired over from Firmino's pass.
With ten minutes remaining, Liverpool again benefited from a break in midfield, Jones advanced but from Robertson's cross Salah thankfully couldn't convert at the back post under pressure from Fleck, who was substituted and replaced by Sharp seconds later.
As three minutes of added time were signalled, Burke latched on to Amapdu's ball over the top, got the better of Phillips, only to be denied by Adrian. United battled gamely until the final whistle but unfortunately without any reward.
Blades: Ramsdale, Baldock, Stevens, Fleck (Sharp 80), Lundstram, McBurnie, Jagielka (Osborn 56), Norwood, McGoldrick (Burke 56), Ampadu, Bryan.
Unused: Mousset, Lowe, Foderingham, Brewster, Ndiaye, Maguire.
Liverpool: Adrian, Alexander-Arnold, Phillips, Kabak, Robertson, Wijnaldum, Jones (Keita 80), Thiago (Milner 76), Mane, Salah, Firmino.
Unused: Ojrzynski, Hughes, Oxblade-Chamberlain, Shaqiri, Origi, R Williams, N Williams.
As it happened...
7:15pm
The players take the knee as a show of solidarity in the fight for social injustice.
United kick-off, and we're underway!
4
Free Kick
Nothing to report as yet here.
United have made a solid start, McBurnie winning a free-kick in a decent position.
5
Save by Adrian!
Norwood with the free-kick, it is a glorious cross and McGoldrick meets it with his head at the back post, pushed away by the 'keeper.
7
Ramsdale did well there...
Ball over the top and Robertson looks as though he's going to win the chase down the left. Ramsdale is quickly out of his goal, but also out of his area, but he intercepts skilfully with his chest and clears.
10
Saved
Brilliant save by Ramsdale!
Ball forward towards Mane falls kindly for Firmino after Ampadu's challenge and he's through on goal but Ramsdale makes a terrific save one-on-one.
He then claws a cross away from right under his bar as Liverpool enjoy their first spell of pressure.
16
Corner
Robertson's cross blocked by Lundstram. Corner.
Cross into the near post, met well by McBurnie, United clear. 0-0.
17
Saved
Cross-field ball from Bryan is good as McBurnie chests down, lays off to McGoldrick who shoots from 22 yards - takes a deflection and Adrian saves...
It's a corner, Fleck takes and Liverpool clear.
19
Ball in behind almost had Firmino in but it's just too strong and Ramsdale is quick off his line and he claims sliding towards the edge of the area.
22
Saved
Ball to the back post is good from Alexander-Arnold and Jones looked in but as he tried to bring it under control, Ramsdale is out to smother ball and United escape.
25
Useful cross into the near post by Bryan, McBurnie moves towards the ball but his effort is blocked.
Stevens then raids into the area but the lay-off just eludes Baldock.
30
Saved
Delicate ball in behind by Firmino and Salah beats makes half-a-yard on Jagielka to shoot but Ramsdale there again to make a save at the near post.
32
Saved
Ampadu with a risky clearance straight to Alexander-Arnold who chops inside on his left before shooting. Tipped over by Ramsdale.
Blades clear the following corner.
36
Goal disallowed for United.
Stevens ball over the top, McBurnie is offside, but Kobak puts it into his own net under pressure from the striker.
Flag raised rightly, free-kick Liverpool
39
Saved
Ramsdale again!
Wijnaldum with the effort from just inside the area, saved by the Blades stopper.
It rebounds to Firmino who has the goal at his mercy but he cuts it back straight to a red and white shirt instead of shooting!
43
Lundstram with a cute ball in behind, lovely idea just slightly too strong otherwise McBurnie would have been in on goal.
45
Half Time
Blades 0-0 Liverpool
Goalless at half-time with Ramsdale making several key saves for the Blades.
45
Liverpool kick-off, second-half underway.
United back out for the second half...
47
Corner
Baldock wins an early corner...
Fleck sends it in, Bryan attacks but he's penalised for a push as McBurnie nods in. Free-kicik Liverpool.
48
VAR Check
United thought that ball had gone out at the by-line as Alexander-Arnold cuts the ball back....play on and Jones fires in!
VAR check...
49
Goal
It's a goal, the whole of the ball hadn't gone out. Liverpool lead.
52
Alexander-Arnold stands up another cross from Jones whose header is saved by Ramsdale.
54
Ball in the net again as Mane converts from Robertson's pass but the flag is rightly raised for offside.
55
Shot
Liverpool really look in the mood now.
Alexander-Arnold weaves his way into the area but shoots wide.
56
Substitute
Double change for United.
Ben Osborn and Oli Burke on for Phil Jagielka and David McGoldrick.
58
Chance!
Norwood with one of those trademark whipped deliveries on the run, but McBurnie heads wide.
62
McBurnie chases the ball over the top and as he's about to pull the trigger, Kabak makes a brilliant last ditch clearance, corner...
63
Shot
Fleck's corner, punched clear to the edge of the box where Norwood drills an effort wide.
2-0.
Firmino weaves his way into the area and shoots. It takes a deflection off Bryan and wrong foots Ramsdale.
65
Goal
67
Shot
Fleck with a run from deep, he shoots, blocked by Phillips.
United corner from Norwood, punched clear again by Adrian.
68
Shot
Burke does brilliant initially as he sprints from a wide position into the area. From a really tight angle he goes for goal and shoots well wide. He had options to cut it back there...
20 yards out he strikes it first time, but fires well over.
75
Shot
Firmino spots Robertson in lots of space on the left.
76
Substitute
Liverpool change.
Thiago off, James Milner on.
78
Salah down the right stands up a cross towards Robertson he heads down tamely and it loops into the hands of Ramsdale.
80
Shot
Close!
Jones carries it, finds Robertson on the outside who puts in a low cross but Salah sends it wide.
80
Substitute
A change each here...
Liverpool bring on Naby Keita for Jones.
United replace Fleck with Billy Sharp.
90
Saved
Late chance for United as Ampadu puts a ball in behind for Burke who gets a toe on the ball but Adrian saves with his legs.
90
Three added minutes.
90
Full Time
Blades 0-2 Liverpool
Second-half goals from Jones and Firmino win the game for Liverpool.