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The Pride Park side, with just one win in six, bounced back from the 4-1 drubbing at Cardiff in midweek, Hulse striking seconds before the break after Sheffield Wednesday had hit the woodwork
Derby, with just one win in six, tested Lee Grant in the opening minutes, Kris Commons' stinging free-kick from 25 yards being stopped by the Wednesday keeper before he snuffed out a cross-cum-shot from Barry Bannan.
Jermaine Johnson powered a shot on the turn over the target before leading scorer Marcus Tudgay almost found a way through, the ball hacked away from under his feet after clever work from James O'Connor.
Derby were foiled by the acrobatic Grant in the 22nd minute, midfielder John Eustace headed into the path of Gary Teale whose fierce volley was pushed round the post by the Wednesday keeper.
Wednesday, whose form at Hillsborough has dipped, were handed a chance, full-back Frank Simek picking out Francis Jeffers with a cross from the left flank, but the former Blackburn striker squandered it looping the ball high over the bar from 12 yards.
Derby escaped on 36 minutes after they failed to cut out Lewis Buxton's teasing cross. O'Connor headed on and Tudgay finished with a volley which cannoned off the back of James McEveley, before Tudgay tried again and this time fired wide.
They had another let-off minutes later, Darren Potter's free-kick from 20 yards crashing off the bar with Stephen Bywater beaten.
Derby broke the deadlock seconds before the break after Commons had been fouled, Teale's free-kick was met by Hulse who lost his marker to head past Grant.
Wednesday were almost level soon after the break, Potter's corner evaded the Derby defence and Tudgay's close-range strike at the near post was deflected by Hulse.
Wednesday manager Brian Laws, a former team-mate of Nigel Clough at Nottingham Forest, threw on strikers Akpo Sodje and Leon Clarke.
Sean McAllister and substitute Etienne Esajas saw their long-range strikes snuffed out by the Derby keeper as the Hillsborough side looked for a way back, but they could not find one.