Neither side created many opportunities with the respective kickers opting to take the points when they were on offer.
A significant headwind made kicking difficult and although Andy Humberstone booted three penalties for Bedwas, Thomas won the kicking battle.
And with James Loxton and Ford scoring tries, it was a deserved win for the capital city side.
Loxton's score had given Cardiff an 11-3 half time lead and in the second half, Thomas booted Cardiff clear with Ford's score adding gloss to the final result.
The first half was certainly a scrappy affair with the boot dominating the game. An eighth minute penalty from Humberstone had put the home side into the lead but against the wind, that was as good as it got for Bedwas in the opening 40.
Thomas missed a long range penalty effort for the Blue and Blacks and with little running rugby on show, kicking for territory was the order of the day. In fairness, neither side had much option other than to kick, the respective scrum halves struggling to get any clean ball away from the contact area.
The kicking contest continued but with Cardiff boasting the left foot of full back Dan Fish, they at least had a different option. Fish and Thomas continued to give Cardiff territory, the first try soon arriving via right wing Loxton. When the score came, it was a reminder of how simple the game can be, Thomas spreading the ball wide for Loxton to execute what was a difficult finish.
The conversion went wide but it was Cardiff who were on top. Fish kept pinning Bedwas back and a couple of Thomas penalties, the first following a powerful surge from No. 8 Luke Hamilton, gave Cardiff a comfortable cushion.
Bedwas had seen hooker Elliot Dee yellow carded in the build-up to Thomas' second penalty, meaning they started the second period with 14. It was a deficit Cardiff took advantage of, Martyn Fowler's side beginning with a bang to extend their lead to 11 points.
Humberstone then added two penalties, either side of a monster kick from Ford and with 15 minutes remaining, it was still anybody's game.
Crucially though, Cardiff looked to be on top in the contact area, the introduction of the experienced Johnathan Edwards giving the Blue and Blacks the edge. And when Bedwas No. 8 Dan Crimmins, a former Cardiff player, was yellow carded, that was pretty much it.
Ford collected a superb Thomas chip to score Cardiff's second try under the posts with the Cardiff fly half converting and adding a fourth penalty to close out the game.
Penalties: Humberstone (3)
Tries: Loxton, Ford; Conversion: Thomas; Penalties: Thomas (4), Ford.