The Bluebirds took the lead as early as the fourth minute when Joe Ralls struck a long-range shot to give his side the best possible start to the game.
The 20-year-old, making his first Championship start of the season, teased the opposition defence before firing a low drive from 20 yards that comfortably beat John Ruddy.
Shellshocked, Norwich were nonetheless able to get back in the game within 10 minutes of the restart, when some prolonged Canaries pressure led to Martin Olsson getting into a good position and firing home from inside the area.
It took just four more minutes for Norwich to peg the opposition back, with Wes Hoolahan smashing the ball into the back of the net from the rebound of David Marshall's point-blank save from Cameron Jerome's header.
The dramatic turnaround was complete when, midway through the second half, Alexander Tettey crossed the ball in for Michael Turner to bundle home, and the away side were able to put the result beyond all doubt with just three minutes left to play when Russell Martin's pass put Cameron Jerome clean through on goal.
The 28-year-old was able to round Marshall to score against his old club and confirm a dreadful afternoon for Ole Gunnar Solskjaer's side.