Toulouse (16) 41
Tries: Medard, Kunavore, Clerc, Bouilhou. Cons: Elissalde 3. Pens: Elissalde 3. DGs: Elissalde, Heymans.
Blues (10) 17
Tries: Spice, Blair. Cons: Blair 2. Pen: Blair.
Maleli Kunavore charges through the Blues defence for a Toulouse try
Toulouse ended Welsh interest in the Heineken Cup with a fine quarter-final display to beat Cardiff Blues.
The Welsh visitors gifted a try to Maxime Medard in the first minute and were then always chasing the game.
A Jason Spice try, later sin-binned as was Toulouse's Cedric Heymans, kept the Blues in touch at half-time 16-10 down.
But Toulouse marched away after the break with Maleli Kunavore, Vincent Clerc and Jean Bouilhou tries, although Ben Blair scored a Blues consolation.
With the Ospreys having lost at Saracens earlier on Sunday in their quarter-final, the Blues took the field at Le Stadium as the last standard-bearers of Welsh hopes in Europe.
But whatever game plan the Blues arrived with was blown within the first minute as Toulouse scored a breakaway try.
Tom Shanklin's attempted grubber under pressure was seized at point-blank range by Kunavore, allowing the Fijian to kick deep into unguarded Blues territory.
Medard had too much of a head-start on Blues wing Tom James and the Toulouse speedster gathered the bouncing ball to go under the posts.
Jean-Baptiste Elissalde stroked the comfortable conversion and soon added a penalty when Maama Molitika carelessly detached too early from a scrum.
Blues could have been forgiven for letting their heads drop, especially when Blair missed an eighth-minute penalty kick that might have helped steady nerves.
But the Welsh showed why they have reached the quarter-finals this season for the first time since becoming a regional side.
A flowing backs move saw James on the left wing show great strength to duck inside Medard and feed Shanklin on his right shoulder.
The Wales centre was brought down just short but scrum-half Spice was on hand to dive over from the ruck, Blair adding the extras to narrow the deficit to 10-7.
Elissalde replied with his second penalty but Toulouse then nearly gifted the visitors a try when Heymans' quick line-out went horribly wrong.
Jamie Roberts got to the ball first and popped a pass to Shanklin, who could not avoid stumbling over his own wing as he went for the try line.
Heymans then killed the ball at the resulting ruck in his haste to atone, earning a yellow card and gifting three points to the boot of Blair.
Back came Toulouse and from the restart the charging French pack gathered for Elissalde to arrow over a cheeky drop-goal and a 16-10 lead.
Full-back Ben Blair gave the Blues brief hope with a second-half try
Before half-time the Blues also suffered a sin-binning, when Spice had a kick charged down and like Heymans compounded the mistake by rushing back to kill the ball.
After the incident-packed first period, the second half started out of character with an attritional struggle in no-man's land.
Toulouse finally broke through thanks to Elissalde, the France half-back adding a penalty before dummying a drop-goal and breaking down the right.
Heymans provided the link and Kunavore rounded the despairing cover to go under the posts for another seven-pointer.
A twin Blues substitution saw the Robinson brothers, Nick and Jamie, take the field and the pair combined brilliantly to send Blair over, the full-back converting his own try.
But any hopes of a recovery were soon snuffed out, as rampaging lock Patricio Albacete punched a huge hole in the Welsh defence that gave Clerc acres of space to add Toulouse's third try.
Elissalde stroked a fine conversion as his final act, leaving the field to a standing ovation with the game won as Valentin Courrent was given the last eight minutes.
Fellow replacement Bouilhou underlined Toulouse's superiority with another try, and Heymans with a drop-goal, as the French advanced to meet London Irish at Twickenham in the semi-finals.
Toulouse: C Heymans; V Clerc, M Kunavore, Y Jauzion, M Medard; J-B Elissalde, B Kelleher; D Human, W Servat, S Perugini, F Pelous (capt), P Albacete, Y Nyanga, T Dusautoir, S Sowerby.
Replacements: V Courrent for Elissalde (73), J Bouihlou for Nyanga (57). Not Used: A Vernet-Basualdo, J Poux, R Millo-Chlusky, M Ahotaeiloa, G Lamboley.
Sin Bin: Heymans (27).
Blues: B Blair; J Roberts, T Shanklin, G Thomas, T James; D Flanagan, J Spice; G Jenkins, G Williams, T Filise, D Jones, P Tito, M Molitika, M Williams, X Rush (capt).
Replacements: S Morgan for Tito (52), N. Robinson for Flanagan (60), J. Robinson for Shanklin (60). Not Used: Yapp, R. Thomas, White, Rees.
Sin Bin: Spice (31).
Referee: Wayne Barnes (Eng).