Cardiff Blues weathered the wet conditions at Adams Park to beat Wasps 18-15 and set up an Amlin Challenge Cup Final with Toulon.
The Blues reached their first European final since the inaugural Heineken Cup in 1996 with tries from Leigh Halfpenny and Gethin Jenkins.
Wasps fly-half Dave Walder kicked 15 points to keep the Guinness Premiership side in touch throughout - but he could not land the vital 77th minute kick that would have taken the match into extra-time.
The Blues had to play the last 10 minutes with 14 men but held out to became Wales' first finalists in any European competition since Caerphilly in the 2003 Parker Pen Shield.
Wasps started with Phil Vickery for the first time since he underwent a neck operation in October while Walder replaced Danny Cipriani at fly-half following last weekend's Guinness Premiership defeat to Bath.
Cardiff were missing number eight Andy Powell but their back row was still formidable and Xavier Rush's ball-carrying was key as the Blues dominated the opening hour.
With just five minutes gone, Cardiff thought they had scored the opening try. Rush barged characteristically through two tackles but his offload was judged to be marginally forward before Blair dived on the loose ball.
Wasps invited further pressure on themselves when Rob Webber flew recklessly into a ruck but Blair pushed his penalty attempt right of the posts.
Dom Waldouck, moved from outside to inside centre, launched Wasps first real attack when he shrugged off Ceri Sweeney's tackle but Mark Van Gisbergen could not hold onto the slippery ball.
Wasps took the lead soon after with a penalty from Walder after Cardiff were caught holding on - but the Blues decamped back downfield and resumed their territorial dominance.
Blair missed a second simple shot at goal but the Blues soon charged into the lead with a well-crafted try from Halfpenny.
Rush created the platform with another powerful run, Maama Molitika took it on before Sweeney changed direction and whipped the ball out wide, where the Wales winger beat Joe Simpson to score.
Blair failed to convert - his third consecutive miss - and Wasps took advantage by earning two penalties which Walder converted in quick succession.
Blair broke his duck with a penalty shortly before the interval but Walder was on target immediately after the restart as Wasps' forwards began to assert themselves.
But the Blues defence withstood wave after wave of Wasps pressure, closing Walder down quickly to deny him the drop goal attempt before bustling Waldouck into touch.
The Blues showed remarkable handling in the conditions to launch an exhilerating counter-attack deep into Wasps territory and earn the penalty shot, which Blair converted.
Wasps were reduced to 14 men when Simon Shaw, having been warned twice in the first half, was sin-binned. Halfpenny missed the long-range penalty attempt but the Blues soon took full advantage of the extra man.
Cardiff launched a powerful lineout drive, pushing Wasps' seven-man pack backwards before Jenkins burrowed over the line to earn the Blues a vital lead.
Blair converted but Walder kept Wasps in touch with his fifth penalty. The Blues were forced to play the last minutes with 14 men when Andrews was sin-binned as the Wasps pack began to dominate.
Another powerful set-piece drive earned Walder a chance to send the match into extra time - but his first miss of the evening confirmed the Blues' place in the final.
Pen: Walder 5
For Cardiff Blues:
Tries: Halfpenny, Jenkins
Pen: Blair 2
Wasps: 15 Mark Van Gisbergen, 14 Paul Sackey, 13 Ben Jacobs, 12 Dom Waldouck, 11 David Lemi, 10 Dave Walder, 9 Joe Simpson, 8 Dan Ward-Smith, 7 Tom Rees (C), 6 Joe Worsley, 5 George Skivington, 4 Simon Shaw, 3 Phil Vickery, 2 Rob Webber, 1 Tim Payne.
Replacements: 16 Tom Lindsay, 17 Ben Broster, 18 Zak Taulafo, 19 John Hart, 20 Serge Betsen, 21 Danny Cipriani, 22 Steve Kefu, 23 Tom Varndell.
Cardiff Blues:15 Ben Blair, 14 Leigh Halfpenny, 13 Casey Laulala, 12 Jamie Roberts, 11 Chris Czekaj, 10 Ceri Sweeney, 9 Darren Allinson, 8 Xavier Rush, 7 Martyn Williams, 6 Maama Molitika, 5 Paul Tito (c), 4 Deiniol Jones, 3 Taufa'ao Filise, 2 T Rhys Thomas, 1 Gethin Jenkins.
Replacements: 16 Gareth Williams, 17 John Yapp, 18 Scott Andrews, 19 Bradley Davies, 20 Sam Warburton, 21 Dai Flanagan, 22 Dafydd Hewitt, 23 Richard Mustoe.
Referee: Romain Poite