Gareth Chapman and Gareth Davies crossed in either half to fire Cardiff into second place behind leaders Llanelli.
With Newport and Neath on cup duty, the title chasers struggled to captialise and trailed 8-7 at the interval at Brewery Field.
But Davies' 44th minute touchdown eased their fears as the star fly-half impressed with a 15-point haul.
Lowly-placed Bridgend had taken a shock lead when centre Gareth Howells opened the scoring for the hosts.
Howells added a penalty before centre Chapman reduced the deficit to one point with his converted try on the half hour mark.
Davies added the crucial try after the interval but Bridgend wing Chris Weightman scored in the 55th minute to keep the hosts in the hunt. But Davies added two further penalties to seal victory.
Nathan Strong's double steered Pontypridd to a convincing win 51-12 in the mid-table battle over Ebbw Vale. Number eight Strong scored twice in the second half as the hosts run riot in a nine-try rout at Sardis Road.
Sam Hobbs, Kristian Baller, Gareth McCarthy, Leighton Davies, Rhys Lloyd, Grant Harrington and Owen Williams also crossed as put the visitors to the sword.
Ebbw Vale had taken a surprise lead when hooker Richard Wilkes touched down but Pontypridd hit back through Hobbs, Baller and McCarthy for a well-deserved 17-5 half-time lead. But the hosts put their foot on the accelerator after the break with half a dozen scores to kill off the contest.
Strong got in on the act after try number four and five by Davies and Lloyd and although Ebbw Vale flanker Simon Pengelly briefly halted the one-way traffic, Harrington and Williams completed a job well done.