With the prospect of a European final in two weeks’ time, Danny Wilson opted not to risk some players, with others nursing short-term injuries following the heroics against Pau.
In total, he made 13 changes to the semi-final side with Gareth Anscombe and Josh Turnbull the only survivors.
You could hardly tell in the first half as Cardiff Blues opened up a 20-13 lead thanks to tries from Anscombe and Smith.
The Ospreys fought back in the second-half with Biggar crossing for his side’s second try and slotting a snatch drop-goal with three minutes to go.
Anscombe got the encounter underway but the Blues were instantly under pressure as Hanno Dirksen fielded the ball and beat two defenders.
He raced deep into Blues territory but Garyn Smith chased him down to make a try-saving tackle on the edge of the 22.
While the immediate danger was averted, referee Frank Murphy soon penalised the home side, with Dan Biggar stepping up to slot a simple penalty.
Cardiff Blues threatened in attack as they worked their way into the encounter with Matthew Morgan causing one of his former team’s problems on the counter.
They were soon level following a long-range penalty from Gareth Anscombe but the Ospreys quickly responded, claiming the game’s opening try on 18 minutes.
A fine break from Jeff Hessler laid the foundations and the pressure told three phases later as Alun Wyn Jones caught the Blues napping at the breakdown to sneak through.
Biggar landed the conversion to give the Swansea-based region a seven-point lead and they continued to put Wilson’s men under pressure.
Cardiff Blues survived the period, winning a superb turnover penalty on their own five-metre line and they soon struck with a try of their own.
Blaine Scully took a quick lineout and moved the ball to Anscombe, who displayed a moment of individual brilliance as he beat three defenders to score.
He added the extras to level the scores and just before the half-hour mark the Blues struck for their second try.
From first phase, Steve Shingler took the ball and threaded a perfectly-weighted grubber, with the outside of his boot, through the Ospreys defence.
Morgan and Smith raced after it with the centre collecting to dive over. Anscombe was once again on target as Wales’ Capital Region opened up a 17-10 advantage
Anscombe and Biggar exchanged further penalties with the Cardiff Blues fly-half hitting the crossbar on the stroke of half-time as the scores remained 20-13.
Four minutes after the restart, and in an identical position, Biggar lined up a penalty after the Ospreys flexed their forward muscle at the scrum but his effort fell short.
The Ospreys dominated the next ten minutes with both Dan Evans and Scott Otten going agonisingly close, the former tackled short by Turnbull and the latter held up over the line.
They continued to press but Cardiff Blues held up manfully in defence, driving the Ospreys back.
That was until Biggar broke a tackle in midfield and evaded the cover defence to claim a fine solo score, which he then converted to tie the scores.
Cardiff Blues remained under huge pressure for much of the third quarter but they soon worked their way into Ospreys territory.
Anscombe kicked a penalty to the corner as his side went for the jugular but the Ospreys snaffled possession and cleared, leading to Blaine Scully going on a stunning counter-attack.
That was brought to a halt by a high tackle from Dmitri Arhip, and while the crowd thought Murphy was looking at that offence, he was actually reviewing an indiscretion at the previous lineout and the Ospreys were penalised.
On this occasion Anscombe pointed to the posts and duly slotted the three points to give his side a slender lead going into the final 10 minutes.
However, the outside half battle continued as Biggar added a penalty before a dramatic drop goal gave the visitors a late lead.