Cardiff City slumped to their fourth home defeat in a row to put manager Lennie Lawrence's job in real jeopardy.
The Bluebirds have failed to score in any of those games and club chairman Sam Hammam will surely now move to make changes at the top.
Derby went ahead in the first half with a superb strike from Marco Reich and they doubled the lead soon after the re-start when Rams skipper Ian Taylor was on hand to punish a defensive slip.
Lawrence made five changes to the City starting line-up with the biggest shock coming up front where rookie Stuart Fleetwood replaced Irish international Alan Lee.
It was Fleetwood who had the first strike on goal after two minutes but his snap shot went wide.
The youngster, who was making his first league start, then had good claims for a penalty turned down in the 11th minute when he seemed to be pushed in the box by Jeff Kenna.
Reich forced Tony Warner to fling himself to his left to grab hold of a shot on the turn midway through the half, but it was City who were looking the more dangerous, with Fleetwood's pace causing the visiting defence problems.
Totally against the run of play the Rams took the lead in the 34th minute. Reich was given time to fire an unstoppable shot in off the far post with Warner a spectator in the home goal.
Five minutes from the break Fleetwood was forced off the field with an injury and replaced by Lee.
City's world fell apart in the 49th minute when Danny Gabbidon tried to find Rhys Weston with a cross-field ball. Reich robbed Weston, but Warner went down well to block his shot. The loose ball ran to skipper Taylor who made no mistake from close range.
Under-fire boss Lawrence brought on Andy Campbell and Paul Parry with 20 minutes remaining and pushed three up front, but the Rams defence dealt confidently with City's attacks to leave the Welsh side in trouble at the bottom of the division.