Derby continued to control the game after the break and Craig Forsyth's free-kick from the left was headed down to Thompson who took it down well, created a yard of space and steered a low shot into the bottom-left corner.
A third soon followed as once more Wednesday lost possession in their own half, a ball down the left was well won by the strength of Brewster whose low cross was cleared only as far as Agyemang to finish high into the net from close range.
Despite almost half an hour remaining, the third goal was enough to send Wednesday fans to the exits.
They missed their side's only chance of the game as Bannan played in Svante Ingelsson, who turned well and shot powerfully with his left foot, but Jacob Widell Zetterstrom stood firm to deny him.
The Rams could have added gloss to the scoreline as Wednesday wilted but were unable to find the final pass, while Pierce Charles' strong save from Kayden Jackson in the final few minutes kept the scoreline just about respectable.
However, the table continues to make miserable viewing for Owls fans. They stay on minus nine points with just one league win all season, and have now conceded 40 goals in their 20 matches.
They are yet to name a preferred bidder with new owners being sought and have been in administration since October.