The visitors started the game well, and Robert Snodgrass gave them the lead in the fifth minute of the contest.
Norwich pushed hard for a late goal, but they could not beat keeper David Marshall, with the hosts claiming a vital win in their battle against relegation from the Premier League.
Here, Sports Mole takes a closer look at the events that unfolded at the Cardiff City Stadium.
On Target 5
On Target 6
Was the result fair?
The final score was incredibly harsh on Norwich, who were in control for much of the match. Cardiff scored both their goals within a minute of each other at the beginning of the second half to completely turn the game on its head. Manager Chris Hughton will be wondering how his team failed to score a second, with a combination of poor finishing and inspirational goalkeeping the difference.
Ole Gunnar Solskjaer will have been delighted to have claimed his first Premier League win as Cardiff manager, but his team were second-best for long periods. The Norwegian must have fired up his players at half time as they started the second period strongly, with new signings Wilfried Zaha and Jones combining well with Bellamy in attack. Solskjaer will have been delighted at the solidarity they showed in defence to hang on in the closing stages and claim the three points that lift them off the bottom of the table.
The last time these two teams met Norwich had 31 shots on goal without scoring, and it was a similar story today. They attempted 27 strikes, but could not add to Snodgrass's early finish. The Canaries hit the woodwork twice, and when they did find the target, Marshall kept them at bay. Hughton will see this as a game his side should have won, and it could prove crucial to their hopes of survival at the end of the season.
Sports Mole's man of the match
David Marshall: Former Norwich player Marshall was impressive once again, as he took on his former side. He pushed an effort from Bradley Johnson onto the bar soon after his side had taken the lead and made stunning saves late on to deny close-range efforts from Leroy Fer and Nathan Redmond. The Scottish keeper has been one of his team's best players this season, and they always have a chance of picking up points when he is between the sticks.
In the third minute of stoppage time, Sebastien Bassong had a great opportunity to equalise for his side, but put a header over the bar from close range. It was not the only poor miss from his team this afternoon, but it proved to be their last big chance to salvage a point.
Mark Clattenburg had a relatively quiet game, as the football did all the talking in this match. Bellamy believed he should have had a penalty in the second half after a clash with Johnson in the box, but the referee made the right call in waving play on. Norwich felt that they had scored when a strike from Redmond found the net, but although it was a tight decision, Clattenburg made the right call to disallow it.
Cardiff: The Bluebirds visit Swansea City for the South Wales derby next Saturday.
Norwich: Norwich welcome Manchester City to Carrow Road next Saturday.