Playing the role of party poopers perfectly, Liverpool ensured that Wilder's first game back on the Bramall Lane touchline would be a frustrating one for the 56-year-old, whose defence was breached by a thumping Virgil van Dijk finish in the 37th minute.
The Blades did not go down waving the white flag, though, and Wilder was left incandescent after Ibrahima Konate escaped giving away a penalty for an apparent shove on James McAtee, before Dominik Szoboszlai doubled the visitors' lead deep into second-half injury time.
While that two-goal defeat is yet another blot on the Blades' notebook, there was a marked improvement from their 5-0 crushing at the hands of Burnley in Paul Heckingbottom's farewell game, although the rankings still make for grim reading for the Bramall Lane faithful.
Indeed, Saturday's hosts remain at the foot of the division with a mere five points next to their name - five adrift of Everton in the safety of 17th spot - and defeat to Liverpool marked a third loss on the trot for Sheffield United in the Premier League.
Van Dijk and Szoboszlai's strikes also saw Sheffield United's goals conceded column tick over the 40 mark - 21 of which have been shipped at Bramall Lane - although seven of their 11 strikes at the correct end being scored at home offers a scant slice of encouragement.
Brentford could also be encouraged by a fast start at Brighton's Amex Stadium on Wednesday evening, where Mbeumo casually sauntered up to the 12-yard mark to give the Bees the lead against the Seagulls in that avian battle, but everything that could go wrong for Thomas Frank's side did go wrong in the hour that followed.
Pascal Gross needed just four minutes to cancel out Mbeumo's effort with a fine strike from the edge of the box, and after losing the sprightly Cameroonian attacker to injury in the latter stages of the first half, Brentford conceded the winner not long after the restart to 18-year-old Jack Hinshelwood.
The Bees did little to trouble a depleted Brighton defence in the time that remained, with Ben Mee trying to channel his inner Alejandro Garnacho with an injury-time bicycle kick but seeing his attempt fly harmlessly wide, as Frank oversaw a third defeat from four matches.
Despite the extremely tight nature of the mid-table places, Wednesday's beating had no impact on Brentford's 11th-placed standing behind West London rivals Chelsea - who are only ahead on goals scored - but five games without a clean sheet may cause some alarm within the Bees camp.
Nevertheless, Brentford's most recent competitive clashes with Sheffield United in the 2018-19 Championship season saw the Bees do the double over the Blades, and they have beaten newly-promoted sides five times in a row in the Premier League, although all five of those clashes came at the Gtech Community Stadium.
Blades striker Oli McBurnie must serve the second of a two-game suspension on Saturday following his sending off against Burnley, and Oliver Norwood has also fallen foul of the rule book, being booked for the fifth time this season in the Liverpool loss.
While Norwood is therefore banned for Saturday's game as well, he was only a late substitute versus the Reds anyway, where all of Daniel Jebbison (illness), Rhian Brewster (thigh), Rhys Norrington-Davies (thigh), Chris Basham (ankle), John Egan (ankle), Tom Davies (thigh) and George Baldock (thigh) were missing.
Most of the Blades' injury victims are expected to be out until the New Year, but Baldock has a slight chance of coming back; Jayden Bogle will be expected to deputise on the right-hand side this weekend either way.
As for Brentford, Mbeumo's seventh goal of the season came an unlucky 13 minutes before the winger was helped off the field with an ankle injury, which will keep the 24-year-old out of action for weeks.
Mbeumo's blow adds to the Brentford injury crisis which Frank labelled the worst he has faced as a manager, as all of Rico Henry (knee), Kevin Schade (groin), Aaron Hickey (thigh), Kristoffer Ajer (foot, Nathan Collins (ankle) and Josh Dasilva (hamstring) are guaranteed to miss Saturday's game alongside the suspended Ivan Toney.
Sheffield United possible starting lineup:
Foderingham; Ahmedhodzic, Trusty, Robinson; Bogle, Hamer, Souza, Lowe; McAtee, Archer; Osula
Brentford possible starting lineup:
Flekken; Roerslev, Pinnock, Mee, Ghoddos; Onyeka, Janelt, Norgaard; Damsgaard, Maupay, Wissa
We say: Sheffield United 0-1 Brentford
With the Brentford doctors working overtime, Sheffield United may feel that the time is nigh to claim another precious three points, especially if Wilder brings the new manager bounce to Bramall Lane.
The Bees will still come into the clash as slight favourites, though, and while their attacking absences should be well and truly felt, Frank's rejigged defence can keep a shot-shy Blades at arm's length to get back on track and deepen their hosts' demotion fears.
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