Despite the red card, the visitors continued to be the better side with Cardiff having to survive sustained late pressure in order to pick up two points and cement third position in the league.
Bulls maintained their winning start to the United Rugby Championship season following a 29-19 win over Ospreys at the Swansea.com Stadium.
The Welsh national team maybe going through a chastening period but there is a rich seam of talent coming through
Jack Crowley kicked 13 points as Munster overcame eighth-place finishers Ospreys 23-7 at Thomond Park to earn a BKT United Rugby Championship home semi-final.
Cardiff were in contention throughout but two tries from international prop Nicky Smith and others from Justin Tipuric and Luke Morgan proved just enough.
The Ospreys No 8 has been a model of consistency for his region but has yet to persuade Warren Gatland he deserves a call-up.
They will need another five-pointer in their final regular season game against Cardiff on June 1 to have any chance of a top-eight finish.
Jordan Larmour scored his first senior hat-trick for Leinster as the Irish province produced a second-half masterclass to hammer Ospreys 61-14 at the RDS.