| Robinson's 12-point haul was crucial as the Blues claimed a league record 16th successive home win, bettering Leinster's previous mark.
Blues winger Rhys Williams scored the only try of the game shortly before the interval, but although Robinson soon had the hosts 14-9 in front, Ospreys number 10 Shaun Connor was left cursing his luck as he missed a late place kick to win it for Lyn Jones' side.
Connor scored all of the Ospreys' points and was in dead-eye form in the first half, sending over one booming effort from 55 metres out.
The fly-halves traded a penalty kick apiece inside the first ten minutes. It was a fast and furious but ultimately scrappy opening period which saw a lack of try-scoring opportunities.
Former Ospreys scrum half Jason Spice was in the thick of the action on his Cardiff debut. O'Connor increased his influence with two further penalties before the Blues struck in injury-time as a fine four-man move ended with flanker Maama Molitika sending Williams over for the night's only try.
Robinson missed the conversion but redeemed himself by belting over a morale-boosting penalty, three minutes after the break. A scrum infringement then saw Ospreys prop Andrew Millward earn a yellow card and Robinson took advantage to put five points between the Welsh rivals.
Connor kept the visitors in touch with his fourth successful kick, only to see Robinson cancel it out with a long range success at the other end. Yet the Blues fly-half struck the post with another shot and watched a drop goal attempt sail wide as Connor replied with another monster effort from near halfway.
That kick set up a grandstand finish but the Blues, last season's runners-up, clung on for the spoils as Connor failed to convert his last-gasp chance.
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