Ole Gunnar Solskjaer's side went into the break trailing by a solitary Robert Snodgrass strike but Craig Bellamy and Kenwyne Jones netted within the space of two minutes early in the second half.
The Trinidadian, signed from Stoke City as part of a swap deal involving Peter Odemwingie, poked home the winner five minutes into the second half to complete a stunning comeback for the hosts, who won for the first time in the Premier League under Solskjaer.
It was Jones' first league goal since December 2012 and came a minute after Bellamy had put Cardiff back on level terms to end a drought of his own and simultaneously set a new Premier League record.
|VIEW FROM WALES
|By Harry Sherlock
It was a tale of two managers here and Chris Hughton will be wondering how his side failed to beat Cardiff this afternoon. Apart from two crazy minutes which saw the home side equalise and then take the lead, Norwich dominated the game and deserved more.
Ole Gunnar Solskjaer, however, will be delighted and rightly so, with his goalkeeper and his defence in fine form. David Marshall made a number of stunning stops and Solskjaer will be glad the transfer window has shut - as such a quality performance from the Scot would surely have prompted a few enquiries in January.
Perhaps the real story is that of Wilfried Zaha. Indeed, David Moyes' loss is very much Solskjaer's gain.
Fabio Da Silva and Jones made their debuts for Cardiff after joining before the transfer deadline while a third addition, Wilfried Zaha, started on the bench.
But it was the visitors who started the brightest - and they were ahead as early as the fifth minute. Martin Olsson broke free down the left and pulled the ball across the box, where it fell nicely for Snodgrass to sidefoot home from eight yards.
Cardiff struggled to make any inroads into the Norwich half, with efforts from distance the best they could muster in the opening half an hour.
Peter Whittingham curled an effort narrowly wide from 20 yards in the 38th minute, before being immediately withdrawn in what appeared to be a tactical switch by Solskjaer, who sent on Zaha in a bid to increase his side's attacking threat.
That change reaped rewards four minutes after the break as Zaha picked up on a loose ball and slipped a pass in for Bellamy, who tucked a neat finish underneath John Ruddy.
And a minute later, the hosts completed a remarkable turnaround, Jones hooking the ball high into the net from close range after his initial header had been blocked.
The visitors came agonisingly close to an immediate response, Bradley Johnson seeing his curling effort from 25 yards tipped onto the crossbar by David Marshall, before Jones almost inadvertently doubled his tally in the 59th minute, deflecting Jordon Mutch's shot onto the outside of the post with his stomach.
But Norwich pressed hard in the final stages, Marshall producing a superb save low to his right to deny substitute Nathan Redmond in the 80th minute, before Bellamy cleared Gary Hooper's effort off the line.
Marshall clawed out Leroy Fer's header and Snodgrass hit the post in the final five minutes as Cardiff held on to lift themselves off the foot of the table, while Norwich are left looking over their shoulder, with just two points separating Chris Hughton's men from the bottom three.