In front of a fired up 11,700 crowd in the Welsh capital, Danny Wilson’s men soaked up huge pressure from a gigantic and star studded French side.
They got off to a flying start as Gareth Anscombe raced over for a stunning try on seven minutes and remained in the ferocious battle throughout.
Conrad Smith hit-back against the run of play and the Pyrenees-based club enjoyed several periods of sustained pressure but the Blues displayed their familiar grit and determination by the bucket load.
Jarrod Evans kept the scoreboard ticking and slotted 11-points in total, including two crucial penalties in the second-half to secure the win.
The victory left a vociferous Arms Park jubilant with verses of Bread of Heaven and Hymns and Arias reverberating around the stands as the Blues claimed a stunning fifth win over French opposition this season.
Cardiff Blues will now travel to Bilbao to face Gloucester, who beat Newcastle Falcons, for the showpiece final.
It took just six minutes for the Blues to strike with Seb Davies galloping through a gaping hole in the Pau defence after hitting a flat-pass from Evans.
There was still plenty for the athletic second-row to do but he displayed plenty of patience as he weighed up his options on the inside and outside as he put Anscombe away.
Evans added the extras to hand Cardiff Blues a healthy 7-0 lead.
Pau’s gargantuan pack attempted to flex their muscle but they were matched in ferocity by Cardiff Blues.
Josh Turnbull made a superb lineout steal on the Blues 22 and the likes of Nick Williams, Gethin Jenkins and Rey Lee-Lo hit hard.
Their forward pressure, predominantly at the scrum, paid off when John Lacey awarded a penalty but Tom Taylor fired wide.
Cardiff Blues continued to carry effectively in the face of a hugely physical Pau side but they were unable to break through as the French side infringed several times at the breakdown without being punished.
The French side’s pressure finally told as Gareth Anscombe’s clearance was charged down by Julien Pierre.
Anscombe managed to dive ahead of the second-row but New Zealand World Cup winner Conrad Smith managed to get a foot in and hacked ahead to score.
Taylor converted but the fired up Blues came back fighting back and threatened on several occasions.
Following a sustained period of pressure they finally benefitted from the whistle of Lacey and Evans duly nudged his side back into the lead.
Taylor levelled the scores once more thanks to the efforts of his pack at scrum-time but Evans kept the scoreboard ticking as Cardiff Blues fought fire with fire.
Once again the Blues made a bright start to the half and they could, and probably should, have scored within four minutes after they worked numbers on the left.
Evans released Lee-Lo but the centre’s pass asked just a little too much of Josh Turnbull and the opportunity went begging.
Pau worked their way back into the encounter and a series of frenetic offloads set alarm bells ringing but the Blues clung on.
Taylor soon had the opportunity to tie the scores once more but his long-range effort sailed wide.
Pau continued to pile the pressure on Cardiff Blues and they dominated both territory and possession for the best part of 10 minutes.
But Wilson’s men weathered the storm as they hung onto their three-point advantage and worked their way out of trouble.
Their defensive effort were rewarded as Evans added a long range penalty to extend the lead to six-points with only a matter of minutes remaining.
Pau kept the pressure until the end, looking for a decisive score, but man-of-the-match, Jenkins, who had dominated the breakdown throughout, forced a crucial turnover, allowing Jarrod Evans to kick the ball dead and seal a place in Bilbao.