Defender Jake Buxton twice headed the Rams level from corners after Lewis McGugan and Will Keane had put the Owls ahead.
And Darren Bent completed the comeback with a penalty after goalkeeper Kieren Westwood was sent off for bringing down Tom Ince.
Wednesday head coach Stuart Gray was disappointed at letting good positions slip away and the sending-off of Westwood, saying: “We have been doing very well in our own box so to concede three goals from set plays was very disappointing.
“Derby are a good side and I think they will get promoted and because they put you under so much pressure we have got lads making decisions with tired minds, but to get ourselves 2-1 up gave us something to build on.
“The disappointing thing in the dressing room was we know how well we have defended our 18-yard box and it’s very rare for us to conceded goals from set plays. And then for Westy (Westwood) to get sent off, I think that was a bit harsh.”