A pair of late goals from Norwich substitute Arturo Lupoli rescued a point for the visitors to Ninian Park after Ross McCormack's double looked to have given Cardiff victory.
Former Motherwell striker McCormack opened the scoring in the third minute, and when he converted a penalty in the 66th minute Cardiff were heading for victory.
But their defence crumbled under pressure and Lupoli levelled the score with goals in the 76th and 81st minutes.
"I was very disappointed with our last 15 minutes," said Cardiff manager Dave Jones.
"After getting ourselves into a winning position the defence switched off.
"We had worked so hard to get two goals ahead and then we were given a slap in the face, but that's football.
"Once you are winning you have to kill off the game but even our experienced players failed to do that."
Cardiff were given the best possible start when Darcy Blake won the ball deep in his own half and threaded a pass to Jay Bothroyd who in turn found McCormack, and the 22-year-old shrugged off a challenge before rifling home beyond David Marshall in the visitors' goal.
Norwich were handed a chance to draw level in the eighth minute when Joe Ledley brought down Matty Pattison just inside the area. Jamie Cureton took the spot-kick but fired wide to give Cardiff a reprieve.
The busy Pattison then appeared to beat Tom Heaton in the home goal but the ball flew off the base of the post and back into the goalkeeper's arms.
Cardiff went further ahead when McCormack was brought down by John Kennedy and got up to fire home the spot-kick.
It was then that the Canaries began to raise their game and it changed dramatically when Lupoli went on as a 74th-minute substitute.
Within two minutes he had reduced the deficit while the Cardiff defence were waiting for an offside flag and five minutes later his diving header went in at the far corner to level the scores.
Delighted Norwich boss Glenn Roeder said: "It was a very strong finish by us and I would have fancied ourselves to score the next goal but on the balance of play we have to be satisfied with a point.
"We needed to do something after going two behind and I'm very glad that we managed to do that thanks to Arturo.
"He has missed all the pre-season work but I thought he could be a late impact player and it has worked out perfectly for him.
"The boys need a pat on the back for keeping going and we are a super-fit side so today it has all paid off."