The 10-man Owls were beaten by the Blades 3-0 in a game essentially won in the first half at Shirecliffe.
The hosts struck three times without reply, leaving Wednesday with a mountain to climb after the break and alas to no avail.
In truth, the Owls struggled to recover from an early blow when United took the lead after just two minutes.
Antwoine Hackford latched on to a loose ball after claims for an earlier foul were waved away and buried hard and low past Alex Hare.
The contest evened out as the opening period unfolded but the next goal was crucial and went the way of the Blades on 27 minutes.
A well-worked move down the left saw Josh Smith deliver an accurate cross from which Theo Williams doubled the lead.
Wednesday poured forward in a bid to reduce the arrears before half time but were hit on the counter on 43 minutes by a Louie Marsh free kick from the right that flew straight into the back of the net after evading a packed penalty area.
The third goal served as a real blow for the Owls and try as they might could not fashion a way through the rigid Blades backline.
It could have been worse too as United were awarded a penalty on the hour when Ryan Viggars went down in the box but Hare sprung to his left to save the same player’s spot-kick.
That was the only real chink of light and to compound a frustrating derby affair, Hall saw red for hauling back Smith on the breakaway with 20 minutes to go and the Owls made the short journey home empty-handed.
Wednesday: Hare, Davidson, Curtis, Yates, Trialist, Aguas, Glover (Kilheaney 80), Ashman, Hall (S/0 70), Zottos (Bradford 70), Cadamatari