The Blades received a standing ovation at full-time against the European champions, having gone toe-to-toe with Liverpool at the Lane.
But unfortunately for United, Georginio Wijnaldum's second-half strike proved to be the difference between the two teams.
For the clash against the Reds, boss Wilder selected the same starting XI that defeated Everton at Goodison Park. There were two changes amongst the substitutes though, with Clarke and Bešić replacing Morrison and Kieron Freeman on the bench.
Liverpool enjoyed plenty of the ball in the opening minutes, but it was the Blades through McBurnie who had the first shot on target, after he'd cut inside Matip from the left. United continued to take the fight to the visitors, Robinson got the better of van Dijk, allowing Stevens to force a corner, but Egan could direct his header at the back post towards goal.
On 21 minutes, United came within a whisker of taking the lead, Fleck picked out the run of Robinson and his shot had the beating of Adrian, only for it to fly inches wide of the far post.
At the other end, Basham snuffed out the danger from Mane, before Stevens was robbed of possession by Salah, who curled an effort wide.
The noise inside the Lane was deafening at times as the Blades again threatened on the break, but with McBurnie lurking from Robinson's clip into the box, van Dijk produced a timely headed intervention, before Robertson threw himself full length to block a shot from Lundstram.
In the 34th minute, the Blades had a huge let off. Van Dijk launched a ball over the Blades defence, but clean through on goal, Mane couldn't control his effort with only Henderson to beat. Robertson then fired wide after United had only half cleared a cross from the right. Moments later, the same player came even closer, hitting the post, after Salah and then Firmino had favourably bounces of the ball go their way.
As one minute of injury-time was signalled by the fourth official, the Blades threatened again, but Matip headed clear ahead of McBurnie after Lundstram had got into a dangerous position at the back post from Stevens deep cross.
Led by Fleck, United were quickly on the front foot at the beginning of the second period, but again van Dijk stood between the Blades and a chance at goal, with Robinson jogging on the spot. The same combination threatened in United's next attack, but again van Dijk intervened.
McBurnie headed over from a promising position from Norwood's flat corner, whilst at the other end there was brief concern as VAR quickly checked a challenge by Lundstram on Mane in the penalty area.
On the hour, Robinson received a warm hand as he was replaced by Mousset and his pace almost paid instant dividends. He chased a pass into the channel before helping create a shooting opportunity for Norwood, which ended with Adrian saving at the expense of a corner. The Blades continued to push men forward. Fleck saw an effort from inside the area blocked, as did Lundstram, before Adrian collected Baldock's cross at the near post.
But on 70 minutes United fell behind, against the run of play. Origi's cross landed kindly for WIJNALDUM whose volley squirmed under the body of Henderson and trickled into the net, but the Blades stopper reacted positively, denied Mane and then Salah in quick succession. And United's number one came to the hosts rescue again moments later, denying Salah who had found himself through on goal after a stray pass by the Blades.
The clocking was ticking down and Adrian was booked for timewasting, before substitute Clarke got in behind van Dijk only to put his effort over the bar from close-range in front of an expectant Kop end.
Four minutes of added time were signalled by fourth official Langford, which gave the Blades hope, but Liverpool saw the game out to cruelly deny the Blades something from a game they were more than it for long periods.
Blades: Henderson, Baldock, Stevens, Fleck, O'Connell, Basham, Lundstram, McBurnie, Robinson (Mousset 60), Egan, Norwood (Clarke 77).
Unused: L.Freeman, Jagielka, Osborn, Moore, Bešić.
Liverpool: Adrian, Alexander-Arnold, Matip, Van Dijk, Robertson, Fabinho, Wijnaldum, Henderson (Origi 63), Mane (Oxlade-Chamberlain 90), Salah, Firmino (Milner 87).
Unused: Kelleher, Lovren, Gomez, Lallana.
As it happened...
We are underway...
United see off the first mini-spell of Liverpool pressure as Henderson's deep cross is eventually cleared. 0-0.
First chance to United.
Driving run forward by McBurnie down the left, he cuts inside and arrows a shot towards goal but Adrian is behind it and makes the save.
Another driving run by McBurnie as he heads into the area, this time the angle is too tight for a shot, and as he attempts to cut it back, Liverpool clear.
This time it is Robinson who carries the attack, he is halted on the edge of the area so decides to play the ball wide to Baldock. His centre is just over the head of McBurnie and Liverpool clear. 0-0.
Stevens' cross put behind for a corner.
Norwood delivers deep to the back post for Egan to rise but it is slightly too high and the Irishman heads wide.
Liverpool half chance as United don't clear their lines properly.
The ball finds Wijnaldum on the edge of the area but his shot is deflected wide and the Blades clear the resulting corner.
Robinson again takes the ball into the area after being found by a terrific pass from Fleck, but he arrows his shot wide. 0-0.
Alexander-Arnold with a mis-directed cross which for a second looks like it might drop in, but Henderson has it covered and watches it over the bar. 0-0.
Stevens loses the ball in a dangerous position but Salah aims his shot a foot wide of the far post. 0-0.
Robinson dinks a cross to the far stick which Van Dijk heads away as far as Lundstram who fires in a fierce strike which is blocked. 0-0.
Huge chance for Liverpool.
A long ball straight down the middle from Van Dijk puts Mane clean through but he skews his effort wide of the near post.
Good spell for Liverpool.
Robertson fires a shot right across goal after United clear to the edge of the area.
Stevens with a brilliant cross to find Robinson's head, but his effort flashes wide.
Mistake by Fleck and Liverpool drive forward.
Out-numbering United, the ball is played to Mane who is clean through again, but he thunders his shot against the post, and Fleck makes a brilliant block to deny an easy follow up. 0-0.
Robinson crosses to the back stick and Lundstram heads into a dangrous area looking for McBurnie, but Liverpool clear. 0-0.
Blades 0 - 0 Liverpool
Second half underway...
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Driving run by Fleck into the area, his low cross is turned behind by Van Dijk who then heads clear from the resulting corner. 0-0.
Teasing low centre looks like it might find Robinson but Van Dijk makes a brilliant interception to clear. 0-0.
Big chance for United!
Dangerous in-swinging corner from Norwood is headed over under pressure by McBurnie.
Looked like a VAR review there for a Liverpool penalty after a challenge on Mane by Lundstram. It is quickly waved away. 0-0.
Alexander-Arnold belts a free-kick well over the bar. 0-0.
First change for United as Robinson makes way for Lys Mousset.
Liverpool change now as Divock Origi replaces Henderson.
Just before the substitution O'Connell was booked for United.
Norwood takes aim from 25 yards and Adrian has to push it away as it dips just in front of him. 0-0.
Chances for United as first Fleck and then Lundstram have efforts blocked by some last ditch Liverpool defending.
Goal for Livepool.
Wijnaldum's shot from the edge of the area goes through Henderson and trickles over the line.
Low shot by Salah on the turn held by Henderson. 0-1.
Norwood is replaced by Leon Clarke for United.
Salah clean through after an error, but Henderson denies the striker making a save with his feet.
Adrian booked for time wasting
What a chance!
Wonderful cross from the left from Fleck and Clarke on the stretch fires over from six yards.
Second change for Liverpool, James Milner replaces Roberto Firmino.
Origi pulls a shot into the side netting. 0-1.
Baldock crosses but McBurnie heads wide.
Four added minutes.
Final change for Liverpool, Mane replaced by Alex Oxlade-Chamberlain
Blades 0 - 1 Liverpool