Cardiff were unchanged from the side beaten at Birmingham City while the Canaries had skipper Adam Drury back in defence for Mark Fotheringham. Starting for the visitors was former Bluebirds keeper Tony Warner.
It only took City three minutes to open their account when Riccardo Scimeca had a shot blocked, the ball rebounded to Parry and he fired into the corner of the net leaving Warner helpless.
Norwich attacked straight from the restart, and when Glenn Loovens failed to clear, Chris Martin lashed a shot high over the bar.
Lee Croft missed a golden opportunity to equalise in the 20th minute when indecision by Loovens and Neil Alexander gave him a sight of goal, but he pulled his shot well wide.
The Bluebirds were well on top leading into the break but they couldn't find the second goal to kill off a very poor Norwich outfit.
The visitors started the second half in more determined fashion and dangerman Darren Huckerby came into the game. He cut inside Joe Ledley and fired in a crisp shot but Alexander was well-placed to save.
The Bluebirds began to look edgy as Norwich searched for an equaliser and passes began going astray. Dion Dublin was brought on in the 54th minute to add height to the Canaries frontline.
A mistake by Parry let Martin through in the 69th minute but his shot went wide of the near post.
A superb save by Alexander from a Simon Lappin free-kick three minutes later kept the Bluebirds ahead and then he tipped over a point-blank header from Dublin as the Canaries kept up the pressure.
Cardiff had to survive an astonishing four minutes of stoppage time during which Huckerby raced in to beat Alexander from close range, but the flag had been raised for offside.
It was not one of Cardiff's better displays but they held out to move back into the play-off positions with their fifth consecutive home victory.
External Reports
The Telegraph
The Times