With only one result possible from the outset, Pontypridd launched the game's first attack through full back Adam Thomas and after winger Jamie Thomas went close to scoring, they opened their account with a try from centre Gavin Dacey.
Swansea responded with a period of pressure but outside half Cameron Clement was off target with two penalties before opening his side's account at the third attempt.
Ponty's response was led by skipper Chris Dicomidis and after applying concerted pressure through some strong scrummaging, lock Craig Locke went over for another close range try, converted by outside half Simon Humberstone.
Pontypridd finished the first half with a 12-3 lead but really made their advantage count after the break.
The second half got underway with Humberstone and Nicky Thomas trading early penalties before the visitors rounded off a period of pressure with a try scored by replacement hooker Huw Dowde. Humberstone converted as his side moved out of sight.
Ponty were kicking for position, setting up camp in the home twenty-two and combining forward drives and wider attacking ploys to turn the screw on their opponents. Pressure was once more turned into points as centre Gary Williams angled in for a well taken, converted try.
Prop Chris Phillips added another score and although the game was over as a contest, Ponty kept piling on the pressure with a series of forward drives.
Wing Rhys Williams claimed a late consolation try for Swansea but it was the visitors who were deserving winners.