It was the 14th league win for Cardiff, but Newbridge put up a brave show and led 17-12 at one point.
Cardiff tries came from forwards James Goode (2), Chris Purcell and James Malpas with a penalty try and other touchdowns from backs Leon Andrews, Richard Jones and Liam Roberts. Andrews converted one and replacement Chris Anderson goaled six.
Newbridge, with several new faces, scored tries by wing Mark Addis and forwards Leighton Davies, Tom Lampard and Stuart Coles with a conversions each by fly half Ross Watts and full back Ross Jones.
Tonight (Wed) Bedwas entertain Pontypridd (7.15pm) with the return at Sardis Road on Saturday.
A special video package as Pontypridd claimed the double for the first time in their history by winning the Principality Premiership final, including match build-up, highlights, post match reaction and dressing room celebrations.