Gareth Jones (2), Matthew Larssen and Luke Ford all crossed for tries for the Blues whilst for the Ospreys' Jason Howells, Rhys Webb and Alex Wilkins scored tries with Leigh Halfpenny adding three conversions and a penalty.
The Blues, for whom Christian Baller added four conversions and a penalty, led 14-10 at half-time and although the Ospreys struck twice in the second half through Webb and Wilkins, they held on for a victory which puts them back on course.
In the other game, the Scarlets and Dragons did well just to survive the horrendous conditions with high winds and heavy rain making life particularly difficult.
The Dragons scored a try through Tom Edwards and there was a conversion and two penalties from Gavin Ashman. However, the Scarlets were too strong and bagged a bonus point thanks to tries from Lloyd Phillips (2), Haydn Pugh, Justin James, Emyr Phillips, NickCudd and Richard Thomas.
Stuart Morris kicked four conversions and a penalty for good measure with high performance manager Darryl Hill admitting, "I have got to take my hat off to both sides, the conditions were terrible from start to finish".
Ron Schottle, the Dragons HPM, said, "We had one or two good performances out there, notably Jimmy Norris, but it was not to be. Had we have scored first in the second half it might have been a different story. Once they pulled away there was no coming back."
In the final games of the group stage on January 3rd, the Blues entertain the Dragons and the Scarlets go to the Ospreys.