Kristian Dacey scored a first half try but it was the boot of Biggar that took centre stage as he kicked Ospreys into a 15-10 advantage at the break.
A second half score from Wales international Justin Tipuric put Ospreys clear before Leigh Halfpenny cut the lead to three points with a series of penalties.
But there was to be no grandstand finale as Ospreys held out Blues in the dying minutes as the hosts had to settle for a losing bonus point and now turn their attention to Dragons on Boxing Day.
Blues were straight on the attack, after Ospreys failed to take the kick-off cleanly, and it was the home side that won a penalty on the floor inside the first minute. Up stepped Leigh Halfpenny and the full back made no mistake as he split the posts.
Scrum half Lloyd Williams saw his box kick charged down by Tom Habberfield, as the Swansea outfit worked hard around the fringes to disrupt the Blues.
Rory Watts-Jones unloaded a big tackle on Sam Lewis before Andries Pretorius drilled back Alun Wyn-Jones with a hit that had the home crowd on its feet. Ospreys held their composure and Dan Biggar dropped into the pocket to slot a sweetly struck drop goal.
Biggar orchestrated a sublime break as he freed his hands in the tackle to send Ryan Bevington into space.
Ospreys came close to the opening try as Biggar charged down the clearing kick from Gareth Davies. But as the Wales No.10 looked to pick up the loose ball and score he was tackled hard by Davies and the ball was lost forward with the line in sight.
Biggar made amends when he slotted over a penalty after 11 minutes, after, the Blues looked to play from deep but were penalised at the breakdown by referee Jerome Garces.
Richard Smith and Robin Copeland combined as Blues looked to respond while Dafydd Hewitt and Halfpenny hunted for holes in the Orsprey’s defensive line.
Ospreys were being given a huge examination as a big home scrum forced them into a mistake. Cuthbert and Kristian Dacey both looked to punch gaps while Davies nearly raced into space.
A penalty was finally awarded, as Ospreys infringed at the breakdown, but Halfpenny made a bad connection as the wind picked up and pushed his effort wide left.
A scrum penalty allowed Biggar to nudge Ospreys further ahead at the midpoint of the half.
However, he went from hero to villain as a knock on by the fly half was made even worse as Ospreys talked their way into giving away a penalty, as referee Garces lost his patience. Halfpenny, though, saw his penalty kick drift right of the target.
Halfpenny looked to make amends immediately as he burst past a tackle with a counter attack and fed Harry Robinson.
Blues raced up in support and when Biggar missed a tackle on Dacey, the hooker picked himself up and powered over from close range. Halfpenny drilled the kick over in difficult conditions.
The home side suddenly had their tails up and looked to strike again. But when they were penalised on the floor for holding on, the visitors took a quick kick and forced Filo Paulo to kick out close to his line.
Biggar was left on the turf after a big hit from Hewitt in midfield but picked himself up to kick into the corner. The home side put in a huge shift to keep the Ospreys out as they twice drilled men back close to the line before forcing the turnover at the breakdown.
Biggar knocked over two penalties before the break as Ospreys took a 15-10 lead into the dressing room.
The home side came out full of passion and pace in the opening stages of the second half and, with the wind causing both teams problems, had an immediate chance with a penalty. The full back read the wind to perfection and cut the lead to two points.
Biggar turned down a penalty chance, and instead opted to the corner in the face of the wind. The move paid off as a driving lineout fractured early, but when it fell into the hands of Justin Tipuric the space opened up and he crashed over.
A series of penalties against Ospreys at the scrum gave Halfpenny a long range shot at goal and he made no mistake from close to halfway.
The scrum problems continued for Ospreys and a yellow card to Marc Thomas followed. Blues suddenly sensed blood and raced up field with a series of crunching runs before the home side secured a penalty and Halfpenny added more to his tally.
Blues made a double change for the final ten minutes with the game still up for grabs, as fit again duo Gavin Evans and Scott Andrews returned. Ospreys, though, were controlling territory well and forcing Blues to play from deep.
Copeland stripped ball in the middle of the park and Williams box kicked in behind to force Ospreys into a lineout close to their own line. A Navidi charge down caused panic and the home crowd were then incensed at a penalty at the breakdown as Blues worked an overlap.
A frantic finale saw Blues look to keep the ball alive at all costs and go wide at pace. But Ospreys held firm in defence to take local bragging rights on the eve of the festive season.
Timeline:
03m Halfpenny p 3-0
05m Biggar dg 3-3
11m Biggar p 3-6
22m Biggar p 3-9
28m Dacey t Halfpenny c 10-9
36m Biggar p 10-12
39m Biggar p 10-15
44m Halfpenny p 13-15
49m Tipuric t Biggar c 13-22
55m Halfpenny p 16-22
61m Halfpenny p 19-22
Cardiff Blues: 15 Leigh Halfpenny, 14 Alex Cuthbert, 13 Richard Smith, 12 Dafydd Hewitt (Evans 69), 11 Harry Robinson, 10 Gareth Davies, 9 Lloyd Williams; 1 Sam Hobbs, 2 Kristian Dacey, 3 Benoit Bourrust (Andrews 69), 4 Macauley Cook, 5 Filo Paulo, 6 Andries Pretorius, 7 Rory Watts-Jones (Navidi 56), 8 Robin Copeland
Replacements: 16 Rhys Williams, 17 Thomas Davies, 18 Scott Andrews, 19 James Down, 20 Josh Navidi, 21 Lewis Jones, 22 Gavin Evans, 23 Chris Czekaj