But both kickers also missed relatively straightforward kicks at goal inside the opening quarter-of-an-hour.
However, a scuffle near to the Blues try-line between Ospreys hooker Richie Hibbard and Blues skipper Paul Tito lit the blue touch-paper to warm up the full house inside the Arms Park.
Hibbard prevented Tito taking a quick line-out and the Kiwi lock seemed to lash out at the Welsh international, who in turn seemed to head-butt the giant Blues star.
It needed some stern words from referee Nigel Owens to calm the situation.
Tito's fellow New Zealander Blair, though, was forced off in the 17th minute with a suspected broken bone in his hand after stopping a Sonny Parker break.
The stop-start showdown burst into life when Tommy Bowe latched on to Biggar's flick pass to set up Byrne for the opening try of the game.
Bowe's burst sliced open the Blues defence and his delicate off-load to full-back-turned-wing Byrne was perfectly timed as the Welsh international dived over for his third Ospreys try of the season.
Moments after Biggar missed the conversion, replacement Leigh Halfpenny, on for the injured Blair, almost replied instantly for the hosts.
The Blues youngster's 30-yard burst was superbly and unceremoniously stopped und by Wales star Gavin Henson, the centre-turned-full-back, just yards from the Ospreys try-line.
However, Nicky Robinson's successful drop-goal from just outside the 22-yard line ensured the Blues held the half-time advantage.
The simmering undercurrent of the game between Wales' top two regions bubbled to the surface again when Tom James appeared to stamp on former New Zealand star Marty Holah when he chased down a kick.
Byrne was sent to the sin-bin for ten minutes after blocking Tom James' path to the line with a superb crunching tackle only to be penalised for killing the ball.
A Nick Robinson penalty extended Cardiff's lead but replacement James Hook, the Wales star on for young Biggar, dragged the visitors back into the game with a penalty of his own.
A great Henson break set-up a Ospreys onslaught and after bombarding the Blues line for a couple of minutes, Hook unleashed Tiatia to bulldoze over the line to complete an excellent comeback for the Ospreys with five minutes remaining.
The Ospreys survived a late Blues rally to end the year on the Magners League summit while the Blues, who have performed superbly in the Heineken Cup and are unbeaten in Europe, have only Connacht below them in the division.
Cardiff Blues coach Dai Young:
"Obviously we were playing a quality team, it was always going to be tight and it could have gone either way but I have to be honest, they did deserve it.
"They edged it, the scrum was a problem for us and I don't think we were accurate enough with the ball.
"We were not in a position to mount enough pressure with the ball in their half and they controlled the game better than we did."
Ospreys coach Sean Holley:
"The score-line was close because perhaps we didn't take as many chances but the difference really was the relentless pressure and some of the attacking rugby we took to the Blues.
"We were rewarded with two good tries and we deserved it but for long periods we were frustrated by some very good Blues defence.
"The intensity was awesome and it gives me goosebumps reflecting and both teams know they've been in a huge game.
"They were passionate about winning the game, I'm hoping the crowd have gone away after enjoying a great Welsh derby because that's what we're here to do as rugby is an entertainment business.
"The league table is a satisfying sight but there is still a long way to go but we've got to be confident because we are in a good position."
Cardiff Blues: Blair, Mustoe, Shanklin, G. Thomas, James, N. Robinson, Spice, Jenkins, G. Williams, Filise, D. Jones, Tito, Molitika, M. Williams, A. Powell. Replacements: Halfpenny for Blair (20), Allinson for Spice (57), Morgan for Tito (57). Not Used: Sweeney, Yapp, T. Thomas, Sowden-Taylor.
Ospreys: Henson, Bowe, Parker, A. Bishop, Byrne, Biggar, M. Phillips, James, Hibbard, A. Jones, Gough, Wyn-Jones, R. Jones, Holah, Tiatia. Replacements: Hook for Biggar (53) Nutbrown for M. Phillips (60), Thomas for Tiatia (76). Not Used: Vaughton, Shervington, Griffiths, Smith.
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