Robert Snodgrass scored the only goal of the first half as Cardiff's woeful run looked like it was set to extend to five losses in their last seven Premier League outings.
But new signing Wilfried Zaha teed up Craig Bellamy for the equaliser just after the break, before fellow debutant Kenwyne Jones fired home the winner at the second attempt a minute later.
It ensured Ole Gunnar Solskjaer secured a first Premier League win since taking charge of the Welsh club which, while not moving them out of the drop zone, got them off the bottom of the table at Fulham's expense.
It was Cardiff's first win in eight league games, and Norwich have now won just one of nine as they remain firmly in the relegation battle having wasted countless chances in a game they fully deserved something from.
Chris Hughton's side wasted no time in taking the lead as Snodgrass neatly tucked away Martin Olsson's cross in the fifth minute after he was released by a fine Bradley Johnson's through-ball.
Johnson's pass left Cardiff new signing Fabio da Silva exposed and Snodgrass took advantage of a disarrayed home defence.
A woefully misplaced backpass from Fabio almost gave Gary Hooper a sight of goal seconds later, and Norwich should really have made more of a spell where Cardiff were all at sea defensively.
Hooper failed to get his head on the end of Russell Martin's excellent cross, before Johnson blazed over after Johan Elmander had easily held off Ben Turner.
After omitting Manchester United loanee Zaha from the starting line-up, Solskjaer withdrew Peter Whittingham midway through the first half to hand a debut to the highly-rated winger.
Zaha made an immediate impact, skipping down the left wing and causing problems for the Norwich defence as Cardiff's attack discovered some much-needed zest.
The anxiety was tangible at the interval, but the game turned on its head within minutes of the resumption.
Cardiff made an inspired return, scoring two goals in as many minutes to cancel out their deficit and take the lead.
Hooper's ball across his own box was seized upon by Zaha, who found Bellamy's angled run for the striker to become the first player to score for seven Premier League clubs.
Just 63 seconds later, Cardiff led.
Jones, largely ineffectual during the first half, lashed home at the second attempt after Martin had blocked his initial header from Craig Noone's cross.
A previously drab contest was suddenly transformed and Johnson thought he was about to equalise for Norwich, only for David Marshall to tip his lofted strike onto the bar.
Cardiff were next to strike the woodwork. Gary Medel won the ball on the edge of the Norwich box and squared to Jordon Mutch.
The midfielder's sliced shot was going wide but struck Jones on the chest and rolled agonisingly against the post.
Another lovely pass from Zaha saw Bellamy go tumbling as he raced into the box, but referee Mark Clattenburg waved away penalty appeals.
Desperate for victory, Cardiff dropped ever deeper during the final quarter, and needed heroics from Marshall to keep them in front.
The Scotland international saved low to his right from Nathan Redmond, who also had an effort ruled out for offside, before Bellamy headed Hooper's effort off the line.
Substitute Leroy Fer worked Marshall again from point-blank range, and Norwich's final chance came and went when Snodgrass headed against the post from a Redmond corner.