It was the first win in three games for the Owls, moving them level on points with second-placed Huddersfield and third-placed Sheffield United.
O'Grady struck first inside the opening 50 seconds when he eased his way unmarked into the box to steer his shot through the legs of goalkeeper Sam Slocombe. It came while Scunthorpe were down to 10 men with full-back Christian Ribeiro off the field needing treatment for a head injury he sustained almost straight from the kick-off.
With Wednesday dominating, O'Grady struck again to make it 2-0, heading home a left-wing corner from Chris Lines. Without a home win now for three months, Scunthorpe rarely threatened in the first half, winger Andy Barcham heading his side's best chance over the top.
Two minutes into the second half, winger Jermaine Johnson made sure of a seventh away win for the Owls when he waltzed his way free into the box to make it 3-0.
Striker Jordan Robertson grabbed a consolation goal for Scunthorpe in the 55th minute when he headed home a left-wing corner from Josh Walker - his first goal for the club. But at the opposite end, only a good save from Slocombe denied Wednesday striker O'Grady his hat-trick.