Two goals in the opening 25 minutes from Mikael Forssell gave Keith Bertschin's side a 2-0 lead going into the half time break.
The Owls pulled one goal back just five minutes into the second half through Jermaine Johnson but Blues held on for a victory which saw them leapfrog Nottingham Forest to top spot in the table.
Blues second string now have just two games to play firstly at Hudderfield Town this coming Wednesday.
Sheff Weds Res: Adamson, McMenamin, Liversidge, Beevers, Hills; McAllister, Folly, O'Brien, Lekaj; Kerr, Johnson (Bradley 59). Subs not used: O'Donnell, Kay, Boden, McClements.
Bues Res: Legzdins, Howland, Price, Pearce, Campion, Dicker (Wilson 78) Kavanagh, Kilkenny, Aluko (Moses-Garvey 89), Forssell, Burge. Subs not used: Joyce, Krysiak, Green.