The visitors took the lead in an evenly-matched contest through Emil Riis Jakobsen’s header early in the second half, but an own goal by Sven Karic brought the young Reds level.
A sucker-punch was served in the final seconds of the match, though, as Mason Bennett surged into space and sent a cool finish past Kamil Grabara to win it.
Derby made the stronger start and should have taken the lead within two minutes.
Corey Whelan’s attempt to nod the ball back to goalkeeper Grabara fell short and allowed Jakobsen to sneak in for a shot that he lofted too high, much to the relief of the home side.