Substitute Nathan Ellington took advantage of a David Marshall howler to earn 10-man Derby a deserved victory.
Derby led through Rob Hulse's bullet header but a Sammy Clingan penalty levelled things.
Keeper Roy Carroll was sent off for hauling down Leroy Lita to hand the Canaries the spot-kick.
But Marshall ran out to a loose ball way too early, gifting it to Ellington, who tapped the ball into the empty net from outside the area.
Norwich manager Glenn Roeder: "A horrible way to lose a game, it's not nice to lose any game but especially to lose in the manner that we did.
"David Marshall's been absolutely brilliant this year, not made any errors whatsoever, and the first error he's made this year he's got punished for.
"You stand and fall by the decisions you make, unfortunately today, for the first time this year, he's made a wrong decision and we've been really badly punished.
"The most annoying thing for me was the way we dropped our pace of play in the second half.
"We had them under real pressure after we'd equalised then we started slowing it down and it made us much easier for their 10 men to play against."
Derby manager Paul Jewell: "We showed the sort of character that was sadly lacking last season.
"If we'd conceded a penalty and gone down to 10 men then we would probably have folded like a pack of cards.
"But full credit to the lads, they showed great determination and great fitness levels as well after the sending-off."
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