The Canaries, unbeaten since their opening day defeat at Wolves, were awful during the first half and deservedly trailed to goals from Joe Ralls and Aron Gunnarsson.
But quickfire strikes from Martin Olsson and Wes Hoolahan levelled matters early in the second half, before Michael Turner and substitute Cameron Jerome finished the job.
Such an outcome had looked highly unlikely as Cardiff, challenged to prove their Championship title credentials by manager Ole Gunnar Solskjaer, raced out of the traps.
Inside a minute Kenwyne Jones had seen his goalwards glancing header hacked clear, but there was no reprieve for Norwich in the fourth minute.
Ralls seized on Turner’s loose pass and drove beyond Alex Tettey to send a left-footed drive into the bottom corner.
It was the young midfielder’s second league goal for the Bluebirds, almost three years after his first.
The visitors were all at sea although Kyle Lafferty almost levelled with a curling strike which David Marshall did well to punch away to safety.
Norwich fell further behind in the 22nd minute. Jones played in Anthony Pilkington down the right, and his cross was expertly tucked home by Gunnarsson.
Having dominated the opening half an hour Cardiff sowed the seeds of their own downfall by surrendering the initiative during the final 15 minutes of the half and, aside from one excellent John Ruddy stop to deny Federico Macheda’s volley, they were not to regain it.
The loss of Fabio to injury weakened the left-side of the Cardiff defence, with Declan John on in his place, and Norwich took full advantage.
Firstly Hoolahan was given far too much room to get a ball into Lewis Grabban in the 54th minute. The in-form striker could not turn Sean Morrison but the ball fell kindly for Olsson to slot home from close range, on the Swede’s return to the side after his ban for pushing referee Simon Hooper.
Four minutes later Norwich were level. Nathan Redmond evaded Ralls and John to deliver a pinpoint cross for Jerome to power a header straight at Marshall, who could do nothing as Hoolahan gleefully dispatched the follow-up.
Cardiff were rocked and they fell behind with 19 minutes to play. Tettey found space down the Norwich right and Russell Martin’s mis-hit shot was turned in by Turner as Marshall appealed in vain for offside.
The Bluebirds responded with Whittingham twice working Ruddy, and Turner being fortunate to only receive a booking after bringing down Nicky Maynard with the substitute through on goal.
But former Cardiff striker Cameron Jerome put the result beyond doubt three minutes from time. Splintering the hosts’ offside trap to round Marshall before tucking home.