Keiren Westwood was sent off on 77 minutes and conceded a penalty in the process that was dispatched by Darren Bent to settle an entertaining clash.
Earlier, the hosts had to twice come from behind with Jake Buxton headers after Lewis McGugan and Will Keane each put the Owls ahead.
But Bent proved the decisive figure and Wednesday could count themselves unfortunate to come away from the iPro Stadium with nothing.
After a cagey and uneventful opening to the game, McGugan delivered what he had threatened since first signing for the Owls back in November.
Twenty minutes in, the midfield man was fouled just outside the penalty area and got up to strike a perfectly placed free kick beyond Lee Grant.
It was a huge boost for the visitors but they almost allowed Derby an immediate route back into the match.
A defensive mix-up saw the ball land at the feet of Tom Ince on the angle but with the goal at his mercy, the loanee striker smacked against the post.
George Thorne then hit a thunderbolt from distance that flew past the post before Kamil Zayatte bravely blocked a well-struck Chris Dawkins effort.
Moments later, Westwood produced a flying save to keep out an Ince set piece as the Rams upped the ante before half time and Wednesday welcomed the whistle.
What they didn’t welcome, though, was a Rams goal a minute after the restart.
Derby won a corner from their first attack and Thorne found Buxton, who glanced into the back of the net.
But the Owls regrouped, the Rams grew frustrated, and were hit on the break on 55 minutes.
Keane broke clear on goal and advanced to drill a firm shot past Grant at the near post.
The hosts made a double substitution on the hour and Wednesday introduced former Rams striker Chris Maguire, making his return from a two-match suspension.
Much of the action was at the other end and Zayatte denied Ince right at the last as the dangerman pulled the trigger.
But the Owls couldn’t hold out and Derby duly levelled on 68 minutes.
The formula was the same as their first goal, only this time Craig Bryson swung in a corner and Buxton was on hand to nod past Westwood.
From that point, the Midlanders went all out for a winner and Ince came close with a clever shot that landed just the wrong side of the post.
But with 13 minutes to go, the contest was settled when Wednesday suffered a double blow.
Westwood felled the menacing Ince who was charging down on goal inside the area and saw red after the referee pointed to the spot.
Bent stepped up to slam past substitute Chris Kirkland and sent Derby to the top of the table and the Owls home pointless.
Derby: Grant, Christie, Forsyth, Buxton, Keogh, Dawkins (Bryson 60), Hendrick, Hughes, Ince, Thorne (Lingard 60), Bent
Owls: Westwood, Palmer, Zayatte, Lees, Helan, Maghoma (Maguire 60), Lee, McGugan, Hutchinson (Kirkland 77), Nuhiu, Keane (Mattock 72)