After creating and wasting several chances early on, the home side scored the only goal of the game when it rolled into the net off unlucky Cardiff keeper Neil Alexander in the 77th minute.
The Canaries defence stood firm from start to finish and the sigh of relief from the home fans was almost audible at the final whistle.
Norwich kicked off attacking the Barclay end and were only inches away on opening the scoring when Andrew Hughes got his head to Darren Huckerby's left-wing cross with the ball going just wide of the post.
Two minutes later Hughes limped off with an injured thigh, to be replaced by Paul McVeigh.
In the 15th minute Dean Ashton set up Youssef Safri, but his long-range effort went inches wide.
Huckerby had a shot saved, then Ashton fired over from six yards when he got a foot to Jason Jarrett's low cross from the right.
Huckerby tried a delicate chip shot but it cleared the bar as well as the keeper.
On the half hour Ashton again fired over and then aimed his header too high as well.
A foul which left Calum Davenport with a bloody nose went unpunished, but a minute later Jurgen Colin was booked for a foul on Jason Koumas.
Safri followed him into the book seven minutes before the break and it was no surprise when Koumas became the only Cardiff player to see a yellow card for his foul on Safri three minutes later.
Jim Brennan replaced Safri, who was suffering with a groin injury, at half-time.
Two minutes into the second half, Alan Lee came on for Michael Ricketts.
Norwich had the best of the second half but failed to create as many chances as in the first.
But in the 73rd minute Ashton created a chance for himself only to fire over yet again.
McVeigh did force Alexander to tip over his long-range shot but referee Drysdale angered the home fans by awarding a goal-kick instead of a corner.
The home side got the deserved winner in the 77th minute. Brennan crossed from the right wing, Davenport headed goalwards and the attempted clearance by Darren Purse rebounded into the net off Alexander.
Colin then had to be carried off and was replaced by veteran defender Craig Fleming in the final few minutes.