The Rams, seeking a seventh straight home win, surrendered their impressive record in front of their own fans as they were breached twice in the first 13 minutes by Chris Martin and an own goal from Shaun Barker.
And despite a goalscoring return to the side for Kris Commons that saw the Scotland international take his tally for the season to 11, County could not battle back.
Commons' return from a sickness bug was one of three changes made by boss Nigel Clough to the Derby side beaten at Burnley, with Dean Leacock also recalled and Gareth Roberts back from suspension.
Wes Hoolahan came in to replace the injured Andrew Surman for Norwich, while there was a return to the bench for Owain Tudur Jones following his three-month loan spell at Yeovil.
Derby's groundstaff beat the big freeze to get the game on, and any fears that the cold snap might affect the pace of the match were soon dispelled by an exhilarating opening period in which Martin and Commons both fired close.
However, it was a combination of bad luck and a goalkeeping gaffe that gifted the Canaries the lead after 11 minutes.
A slick passing move involving Henri Lansbury, Hoolahan and David Fox stretched the home defence, working space for the latter to shoot at goal.
Fox's piledriver nicked off the boot of Barker on its way through, but goalkeeper Frank Fielding still should have done better as he failed to get his body positioned properly and the ball slipped through his grasp and into the net.
If there was a degree of good luck about that opener, there was certainly nothing fortunate about the visitors' second goal two minutes later.
More slick passing opened up the Rams rearguard, setting Simon Lappin free on the overlap. He burst toward the byline and clipped a pass into the area, where Martin was on hand to head home his sixth goal of the season.
Derby's proud home record was wobbling, but they made the perfect response after 17 minutes when Commons ran off the shoulder of his marker to latch on to Luke Moore's flick and steer the ball into the corner.
Paul Green almost levelled matters after 21 minutes, only for Norwich goalkeeper John Ruddy to deny him with a superb save.
Commons' influence continued to grow throughout the first half, and 11 minutes before the break he was almost rewarded for another purposeful run when his shot flew just wide.
That signalled a spell of Derby pressure, and after the interval they picked up with more possession - Tomasz Cywka twice firing close as they went in search of an equaliser.
Green was then denied by a superb save from Ruddy at the far post after 66 minutes as the shot-stopper reacted smartly to keep out his close-range stab at goal.
Grant Holt - surprisingly quiet for much of the afternoon by his standards - forced a reaction stop from Fielding at the other end 11 minutes later, before Andrew Crofts lifted a shot over the crossbar.
But there was still time for a gilt-edged chance to fall Derby's way when the ball rebounded back to Commons with seven minutes left.
The Scot found himself with a clear sight of goal after skipping past Elliott Ward and Leon Barnett, but he somehow managed to blast his shot wide.