Keeper David Marshall might have done better with Derby's first-half opener and could certainly be blamed for substitute Nathan Ellington's winner in the 85th minute.
In between these goals, Roy Carroll was sent off five minutes into the second half for a foul on Leroy Lita and Sammy Clingan scored his first goal for City from the resulting spot-kick.
Norwich kicked off attacking the River End goal, but suffered an early setback when their captain for the day, Darel Russell, was booked for a foul on Miles Addison.
Marshall did well to block a fierce angled drive from Steve Davies.
After 15 minutes, Paul Connolly appeared to use a hand to keep out a low first-time shot from Omar Koroma.
In the 19th minute, Lee Croft's low, right-wing cross reached Koroma on the far side of the penalty area but he fired wide.
Derby took the lead when Rob Hulse headed in a right-wing corner from Davies at the far post
Jordan Stewart then put in a useful left-wing cross, but Davies could only glance his header wide of the far post.
There was a dramatic start to the second half when Carroll was sent off for the foul on Lita and Clingan stepped up to convert the resulting penalty with his right-foot shot beating substitute Stephen Bywater 's dive to his right.
For a few minutes it looked as if the home side would turn their numerical advantage into a winning goal, but the Rams soon re-organised and kept the home side at bay until five minutes from full-time.
Then Stewart's long punt up field found Ellington, who capitalised on Marshall's ill-judged rush to the edge of the area to net the winner with a cool finish from 18 yards.
In the 90th minute, Lita fired wide and even five minutes of stoppage time was not sufficient for the low-flying Canaries to salvage a point from a game they should have won.