Adam Reach put the home side in front before Derby hit back with goals from Harry Wilson and Jack Marriott to leave the Owls without a win in six games.
"I think in the first 30 minutes we played very good and came strong in the game. We made a good first goal from Adam and we tried to put pressure on," said OWls boss Jos Luhukay afterwards.
"We lose after the 30 minutes. In five minutes, we gave away two goals too easily due to individual mistakes. We had a difficult time in the last 10 minutes before half time.
"In the second half, we tried to come back in the game. The team gave everything to the last minute and I think there were two or three very good chances to make the second goal.
"Fernando had maybe the best chance to score and Morgan Fox with his header to the post. We have not scored in the second half the important goal to come back.
"It's very frustrating when we look back on the last six or seven games and see how easy we give goals away."
Lucas Joao, one of three players restored to the Wednesday starting line-up by manager Jos Luhukay, put an early effort wide before the home side took the lead.
The goal came in the 12th minute when Barry Bannan's lofted delivery into the area found Reach on the right-hand side and he slotted the ball past Scott Carson from a narrow angle.
Fernando Forestieri, making his first start since early October, fired a free-kick on target but it was no test for Carson, who gathered the ball comfortably.
Derby equalised in the 29th minute when Duane Holmes found Marriott inside the area and when his effort was blocked, the ball fell to Wilson who hammered it beyond Cameron Dawson.
Marriott put Derby in front six minutes later when he received the ball from the recalled Florian Jozefzoon, got in between a couple of defenders, advanced into the area and slotted past Dawson.
After Morgan Fox headed over from Forestieri's corner, Derby went close to adding a third in first-half stoppage time when Marriott's effort hit the bar.
Derby boss Frank Lampard made a change at the break, sending on Curtis Davies in place of Fikayo Tomori. Forestieri wasted a great chance after receiving the ball from Reach, shooting wide from a good position inside the area.
Wednesday enjoyed a good spell of possession and they went close to an equaliser when Fox headed against a post. Derby threatened soon after when Tom Huddlestone fired in an effort from 30 yards which was well saved by Dawson.
Luhukay made two quick substitutions, sending on Atdhe Nuhiu and Matt Penney to try and find the equaliser. But despite continuing to have plenty of the ball, Wednesday struggled to put the opposition defenders under strong pressure.
Reach managed to get a shot on target from around 20 yards out but Carson was equal to it, getting down low to his left to make the save.
In the closing stages, Marriott had a shot deflected wide as Derby looked to kill off any hopes the hosts had of staging a revival.
Derby appeared content to sit on their lead and rarely ventured into opposition territory in the latter stages with the final whistle prompting some boos from the home crowd.