The Ospreys scored three tries through lock James King, full-back Richard Fussell and replacement flanker Morgan Allen for a win which lifted them into fourth place in the table.
The Blues only managed two penalties apiece for fly-half Ceri Sweeney and full-back Rhys Patchell.
Both sides were without key players for such an important Pro12 game, but it was the Ospreys who made the much better start as they scored 13 unanswered points and went into a 16-6 interval lead.
A good scrummage from the Ospreys earned them a penalty after 10 minutes which lively Morgan kicked.
The Ospreys continued on the front foot as they scored a converted try only three minutes later.
King went in at the corner after originally winning a line-out, with scrum-half Kahn Fotuali'i and Joe Bearman involved in the build-up.
Morgan kicked a second penalty on 24 minutes after the Blues came in from the side at a maul.
That kick was cancelled out by a Sweeney penalty two minutes later from the Blues' first real attack of the match.
The Ospreys' edge in the scrum earned a penalty in the Blues 22 which Morgan kicked to restore a 13-point lead three minutes before half-time.
But just before the break and against the run of play Sweeney converted his second penalty.
Only two minutes into the second half the Ospreys secured a second try when Fussell went over following up a neatly weighted kick ahead by wing Ross Jones.
The Blues did launch something of a comeback with two Patchell penalties - the second one which came about after Sam Lewis was sin-binned for a professional foul.
But despite going down a man the Ospreys scored next with Morgan slotting a fourth penalty.
The Blues found themselves with more territory in the final 15 minutes but could not make it count on the scoreboard.
Following the sin-binning of captain Josh Navidi, Allen scampered over for the Ospreys' third try which was converted by Morgan.
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