Glenn Loovens suffered a horror return to Sheffield Wednesday's line-up after he was sent off inside the opening five minutes.
Owls captain Loovens - back in the side following injury - hauled down Matej Vydra and was red carded by referee Scott Duncan.
Vydra netted from the spot, and despite a much-improved Owls performance, they could not pinch an equaliser and Bradley Johnson wrapped up the points late on.
Owls chief Carlos Carvalhal made three changes from the side which lost at Bolton last time out, goalkeeper Kieren Westwood, captain Loovens and left-back Morgan Fox coming into the team.
There was also a place on the bench for winger Marco Matias, but Sam Hutchinson or Daniel Pudil were not in the match-day squad.
The hosts should have been 2-0 up - after the Owls had their own penalty appeals for handball rejected - when Tom Lawrence burst through, chipped the ball over Kieren Westwood, only to be denied by the post.
Derby looked dangerous in attack, but the Owls had their chances. Steven Fletcher's header set Gary Hooper free, but he was denied by a Curtis Davies tackle.
Then Fletcher got on the end of Ross Wallace's corner, but headed just wide of the post, before going down in the penalty box when clean through - but again referee Scott Duncan waved away claims for a spot-kick.
At the other end, Westwood had to be alert to keep out Johnny Russell's long-range effort.
Derby dominated for long spells in the second half, as they pushed for a second goal.
Buit the Owls were dangerous on the break, Scott Carson doing well to deny Barry Bannan, who also went close with a 30-yard drive.
Substitute Chris Martin's header looked goal-bound, but Westwood struck a foot out to divert the danger.
Yet the Owls goalkeeper was left helpless when Bradley Johnson turned and fired in, after good work from Russell down the right flank.
Owls played with 10 men for 85 minutes and put in a performance which was a big improvement on previous weeks.
Skipper Glenn Loovens now suspended, and plenty of work for Wednesday to do on the training ground.
But this was a defeat where they can walk away with their heads held high.