Sturridge struck on 23 minutes and his side were able to hang on in the face of fierce pressure from the Owls in the final half an hour.
The South Yorkshire side may feel hard done by in suffering their second defeat in succession as they dominated after half-time and claimed Sturridge's strike should have been disallowed for offside. But Derby will take whatever they are given. They are now unbeaten after four Premiership matches and sit proudly in the higher echelons of the table at this early stage of the season.
Last term the Rams beat Wednesday 5-2 at Hillsborough and 3-0 at home in what their manager, Jim Smith, described as his side's best two performances of the campaign. Last night's Derby display was hardly vintage stuff, but it was good enough for three points.
The winner came when Des Walker got his head to Rory Delap's long throw, but the ball found its way to Lee Carsley 20 yards out. He nodded it back into the area, where both Sturridge and Wanchope looked to be offside. Sturridge controlled the ball on his chest before volleying it beyond Kevin Pressman from six yards.
Derby County: Hoult; Schnoor, Stimac, Sturridge, Delap (Kozluk, 90), Bohinen (Eranio, 70), Laursen, Wanchope, Prior, Carsley, Baiano (Powell, 70). Substitutes not used: Poom (gk), Burton.
Sheffield Wednesday: Pressman; Atherton, Jonk, Walker, Whittingham (Briscoe, 76), Carbone, Booth, Cobian (Barrett, 89), Hinchcliffe, Thome, Rudi. Substitutes not used: Hyde, Clarke (gk), Sanetti.
Referee: P Jones (Loughborough).Reuse content