The home side enjoyed much the better of the first 45 minutes and could easily have added to Dickson Etuhu's seventh minute goal by half-time.
As it was, Cardiff had a lot of second-half possession without getting the better of a well-organised Norwich defence.
The visitors started brightly and Norwich keeper Jamie Ashdown, signed on loan from Portsmouth on Friday, was nearly tested as early as the third minute only for Steven Thompson's shot to fly inches wide.
At the other end Etuhu's shot was firmly held by Neil Alexander. However, the Norwich midfielder found the back of the net in the seventh minute when he curled a right-foot shot inside Alexander's left-hand post from some 25 yards.
In the 20th minute Darren Huckerby 's shot was blocked by the keeper and eight minutes later Rob Earnshaw, playing against his former club, jinked his way into a good shooting position only to fire wide of the target.
Norwich's Carl Robinson was only inches away from making it 2-0 with a fierce drive before Huckerby set up Earnshaw who shot straight at Alexander.
Just before the break the Cardiff keeper again denied the Norwich striker in a one-on-one situation.
Bluebirds boss Dave Jones brought Malvin Kamara on for Luigi Glombard at half-time with Paul Parry moving from right wing to striker.
The visitors stepped up a gear in the second half and in the early stages both Lee Croft and Adam Drury were booked for fouls.
Huckerby made way for Paul McVeigh and Kevin Campbell replaced Thompson but neither side was able to fashion a worthwhile scoring chance.
Joe Ledley was replaced by Willo Flood and promptly got himself booked for a foul on Croft.
As the game went into five minutes of stoppage time Youssef Safri limped off to be replaced by veteran striker Dion Dublin and Kerrea Gilbert and Paul McVeigh were sent off for squaring up to one another in the dying seconds.