They will also display that it occurred against the two sides widely perceived to be the best in the land in reigning title holders Manchester City and the side who increasingly have the look of champions-elect in Liverpool.
History was firmly against the Blades in their outing against indomitable hosts.
Here was a side with the incentive of not just moving 13 points clear at the summit with victory, but also going a whole year without sampling a top-flight loss, which they duly chalked off after extending their unblemished record to 37 matches since losing at the Etihad Stadium on January 3, 2019.
That represents Liverpool’s only setback in their last 59 Premier League outings, while Jurgen Klopp’s red machine now boast an unbeaten 51-game league record at fortress Anfield.
Their 18th successive home league triumph was routine enough, although Chris Wilder would have had cause to rue the hosts’ early opener.
After Dean Henderson’s costly error proved the difference in the reverse fixture at Bramall Lane, a fourth-minute slip from George Baldock proved fateful as Andrew Robertson was able to race away and supply Mo Salah for the sort of chance he was always going to convert.
It did take Liverpool until the 64th minute to nail down the points from Sadio Mane, but in truth, it was a largely comfortable evening.
It was park life as opposed to the high life that the Blades sampled ahead of this appointment, having staged a gentle warm-up session in Stanley Park in the morning of the game – with Anfield in full view.
It represented a reminder of how far they have travelled under the command of Wilder.
His opposite number was full of admiration for the Blades in his programme notes, referencing an ‘amazing story’ with ‘a few more chapters to come, clearly.’
Three years to the day since United took the field in a league fixture at Bury, they found themselves in exalted company, with a stirring chorus of their ‘Greasy Chip Butty’ signature tune, which competed with the famous ‘You Will Never Walk Alone’ home anthem ahead of kick-off, indicative of their defiance.
A few minutes in and it had all the portents of a long evening after the hosts’ soft opener, but the Blades’ response was admirable enough.
United had their moments, certainly when boyhood Reds supporter John Lundstram almost quietened the Kop with a looping shot which sailed inches wide just after the hosts’ opener.
Alisson Becker was also kept honest when he was forced to tip over a rising strike from David McGoldrick.
Most of the other action was reserved for the other end and while Liverpool’s final ball and option let them down at times, they possessed customary menace through their feted front three.
A brilliant one-handed save from Henderson to tip over Salah’s crisp strike provided a memory to treasure, with him also beating away a fierce strike from the Egyptian at his near post after a raking crossfield pass from Trent Alexander-Arnold.
The Blades may have been left to contemplate an interval deficit, but their task in the second half was not insurmountable.
An early scare on the resumption saw Virgil van Dijk, who produced an immaculate challenge to deny Lys Mousset ahead of the interval, almost get on the end of a viciously whipped-in free-kick from Robertson as the hosts sought a second goal.
It almost arrived when the hitherto quiet Roberto Firmino cut inside on the left and saw a ferocious curler whizz inches wide.
A dinked cross from Salah evaded everybody and hit the post before being gratefully grasped by Henderson, but it wasn’t too long before he was picking the ball out of the net in front of the Kop.
A dazzling interchange between Salah and Mane ended in the latter seeing his toe-poke blocked by Henderson, with the Sengalese striker tucking away the rebound.
It was the moment of quality that Liverpool were always likely to unleash from their locker at some juncture and effectively sealed the game as a competitive entity.
Firmino was inches away from a third before Henderson did well to keep out Salah’s low strike as Liverpool suddenly found their swagger, with Becker thwarting Oli McBurnie in his quest for a late consolation.
Liverpool: Alisson; Alexander-Arnold, Gomez, van Dijk, Robertson (Lallana 88); J Henderson, Wijnaldum, Milner; Mane (Origi 78), Salah (Elliott 90), Firmino. Unused substitutes: Adrian, Williams, Phillips, Jones.
Sheffield United: D Henderson, Basham, Egan, O’Connell, Baldock, Lundstram, Norwood (Besic 78), Fleck, Stevens, McGoldrick (Sharp 66), Mousset (McBurnie 65). Unused substitutes: Jagielka, Verrips, Osborn, Robinson.
Referee: P Tierney (Lancashire).