A tight game saw Cardiff go close inside the opening seconds when Jay Bothroyd slotted the ball wide when in on goal but overall Cardiff were good for their victory.
Looking back on the match Swansea were reduced to efforts from distance and hardly any, if any at all troubled Tom Heaton who had his quietest game for a long while.
The clean sheet kept by City was the first since Boxing Day and we are now unbeaten in the past 5 games, a run that has seen wins over close rivals Leeds, Watford and Swansea and draws against Reading and Norwich.
The better chances in the game fell to City with Paul Quinn missing a couple of headers, Chris Burke and JET snapping at shots that went wide.
There were two moments of sheer class though. Darcy Blake, on as a sub for the injured Kevin McNaughton at half time, danced his way through the Swansea defence to see his effort smack the post before the winner from Bellamy.
Aaron Ramsey pushed the ball down the right to Bothroyd whose cross field ball found Bellamy 25 yards out. He played a one - two with Aaron Ramsey who laid it up for Bellamy to curl one in off the post from the very spot of Bellamy's first touch. It was a cracker and turned out to be a deserved match winner.
Cardiff saw out the game with little fuss and have moved upto 3rd in the table.
That was a crucial win for City and they came through their derby day test with flying colours.
Next week we have a home double header with Scunthorpe and Burnley at the CCS on Feb 12th and 15th respectively.