Derby take a 2-1 lead into the break after goals from Nathan Tyson and Jake Buxton.
Tyson grabbed the first goal of the Rams' new season on 11 minutes after tucking the ball past Chris Kirkland. Buxton doubled the lead after 27 minutes with a header from inside the box.
Chris O'Grady halved the deficit for Wednesday with a well-struck effort from the edge of the area six minutes before the break.