In a game of few chances the game was defined by two big saves, one apiece from goalkeepers Keiren Westwood and Dean Henderson, to deny Gary Madine and Sam Hutchinson respectively.
United, who recalled Jack O'Connell, Chris Basham and former Owl Madine, will feel they slightly edged the first half and certainly created the best chance, when Madine got his head to Oliver Norwood's beautiful cross but couldn't beat Owls goalkeeper Keiren Westwood who saved well with his body.
Owls' talisman Fernando Forestieri failed to reappear for the second half, replaced by George Boyd, and Blades skipper Billy Sharp was inches away from a good chance from Norwood's cross-cum-shot.
United goalkeeper Dean Henderson was forced into his first save of the game when Sam Hutchinson met Rolando Aarons' excellent cross from the left, and the Newcastle loanee raised Wednesday hearts in stoppage time when he let fly from long range, only to see his shot sail over Henderson's bar.
Sheffield Wednesday boss and chairman unhappy after attackers leave for Premier League
Sheffield Wednesday injury update on Michael Smith, concerns cooled over defensive pair
‘One or two wilted’ – Sheffield Wednesday to learn from last year as Darren Moore makes brutally honest transfer admission
Sheffield Wednesday identify two possible striker transfers – meeting to be held to discuss next steps
Sheffield United Player Ratings: One man stands out as star man as Blades bow out of cup at West Brom
Full match report to follow.
Blades: Henderson, Freeman, Basham, Egan, O'Connell, Stevens, Fleck, Norwood, Dowell (Cranie 62) Sharp, Madine (McGoldrick 68). Subs: Hogan, Coutts, Stearman, Duffy, Moore.
Wednesday: Westwood; Iorfa (Fox 79), Lees, Hector, Palmer; Reach, Bannan, Hutchinson, Aarons; Forestieri (Boyd 46) Fletcher (Nuhui 90). Subs: Dawson, Pudil, Pelupessy, Matias.