Castres will now meet Toulouse for a place in the 2011-12 season finale.
The eventual winners flew out of the blocks and were ahead after just two minutes when Pierre Bernard slotted the first of his five penalty kicks on the night.
Castres suffered a potential set-back soon after when scrum-half Thierry Lacrampe was sin-binned but they shrugged off the blow to go 6-0 ahead through Romain Teulet in the 15th minute.
Lacrampe returned to go over for his side's only try of the game to make it 13-0 before Martin Bustos Moyano finally got the Montpellier on the board.
That gave Montpellier a shot in the arm and when Alex Tulou went over in the corner, it seemed they were back in the game.
But Bustos Moyano missed the conversion and another kick at the other end from Teulet saw the half-time scoreline read 19-8.
Bernard continued his accuracy with the boot after the break to take Castres 25-8 up but another glimmer of hope was offered to Montpellier when Joe Tekori was dismissed for a high tackle.
Again, Montepellier went over, this time substitute Aliki Fakate crashing over with 11 minutes remaining.
But it was too little too late as Teulet and then Bernard added further penalties to secure Castres' passage into the final four.