Derby's first goal arrived on 17 minutes as Lee Croft drove in off the bar from six yards after Paul Dickov had cleverly turned a defender to help on Jake Livermore's cross.
Dickov - in his first start since arriving on loan from Leicester City - almost made it two for the Rams when just before the break he shaved a post with a crisp drive from ten yards.
The Owls should have levelled on 55 minutes when a horrible blunder by Dean Moxey allowed James O'Connor to feed Leon Clarke, who blasted over from eight yards with just the keeper to beat.
Wednesday went close again when a long clearance from Lee Grant was headed on to his own bar by Shaun Barker.
Derby went two up on 65 minutes when Croft found Jay McEveley who let the ball run before drilling a shot beneath the keeper from 14 yards.
Derby wrapped up the points with a third goal in time added on when Lewis Buxton upended Rob Hulse inside the box, with the Rams striker dusting himself down before slotting home the penalty low to the keeper's right.