Burley's men had beaten Town 3-2 at Pride Park in August and they went ahead after just seven minutes, Tommy Smith's shot being deflected perfectly for Marcus Tudgay to loop a header over Kelvin Davis.
Morten Bisgaard fired wide from a dangerous low Smith cross before Shefki Kuqi lifted the ball over from close range after Darren Bent had fired in a cross from the left.
Town came close to an equaliser on 22 minutes when Darren Currie's header was met by a thumping Richard Naylor header which cannoned away off the bar, while Tommy Miller's follow-up was charged down by Tom Huddlestone.
From that let-off, Derby broke quickly and should have scored, Polish striker Grzegorz Rasiak heading over from the edge of the six-yard box from Smith's cross.
Town were level on 22 minutes, skipper Jim Magilton scoring his first of the season with a shot which deflected in off Jeff Kenna, having been set up by good approach play from Kuqi and Bent.
Naylor was unlucky again with another header from a Currie cross, Adam Bolder this time blocking it on the line, Currie then curled a dangerous free-kick just wide and the same player's cross was headed back by Bent, but fell in between Kuqi and Magilton.
Town were ahead just 11 seconds after Derby kicked off the second half - Miller playing the ball through for Bent to run clear and clip home his 16th goal of the season.
Bisgaard could have equalised on 54 minutes when he ran in behind Fabian Wilnis on to a Rasiak flick, but blazed well over when he should have done much better.
Davis saved a curling Inigo Idiakez free-kick, then Ian Westlake curled an effort wide and Derby keeper Lee Camp denied Bent's powerful low drive.
Kuqi was unlucky on 68 minutes when Miller and Bent combined to give him a sight of goal from just inside the area, but although his power-packed drive beat Camp, it clipped the bar and went over.
A third goal was coming and it arrived on 71 minutes, Pablo Mills blocking Kuqi's diving header from another Currie corner, but Miller fired home the rebound from 16 yards.
Sub Paul Peschisolido had a curling shot saved by Davis immediately after the goal and the game seemed to be petering out for a comfortable Town win until the Rams scored with five minutes left.
Smith flung over another good cross and Idiakez arrived beyond the far post to direct an unstoppable header beyond Davis.
Derby had one final chance in the third and final minute of added on time, Bisgaard getting his head to a curling Idiakez free-kick, but Davis was able to dive and save.