The Rams had David Jones to thank for two superbly-taken goals which took his tally to five for the season.
But Norwich were not helped by two controversial refereeing decisions. Darren Huckerby went down towards the end of the first half when Marc Edworthy clipped his heels but no penalty was awarded.
In the second half, Chris Martin saw his second effort ruled out by a dubious offside decision.
The first half was played in a competitive but sporting fashion. Unfortunately the second half turned out to be less so.
The visitors kicked off attacking the River End goal, but had their keeper to thank in the early stages when he stopped three shots in the first six minutes.
In the 12th minute, Andy Hughes saw his goalbound effort blocked by a defender.
Giles Barnes had a shot saved by Tony Warner, while at the other end Darren Moore did well to halt Huckerby's run into the penalty area with a well-timed tackle.
Craig Fagan's shot was saved by Warner before Youssef Safri curled a free-kick just wide.
Edworthy then marked his return to Carrow Road with a crude challenge on Martin which brought the first yellow card of the game.
Huckerby went down in the Derby penalty area when Edworthy tapped his ankle but referee Lee Probert awarded a goal kick.
Arturo Lupoli brought a good save from Warner before Norwich took the lead. Martin's low right-foot shot from 18 yards beat Bywater's despairing dive to his right.
Gary Teale made a significant difference to the game when he replaced Fagan just before the hour.
Martin then appeared to have put the Canaries back in front, but the celebrations were cut short by a late offside flag.
The decision seemed to lift Norwich, but it was the visitors who scored next to grab all three points.
Teale's left-wing cross was laid off by Barnes to Jones who gave Warner no chance with a fierce left-foot shot from 12 yards that beat the on-loan Fulham to his right.
Dion Dublin came on for Etuhu and brought an acrobatic save from Bywater with a blistering drive and the Rams held on for the points which took them back to the top of the Championship.