Antonie Claassen's try proved critical as Castres earned a match against Clermont in the second semi-final on May 25.
A tense opening half saw Castres' Rory Kockott and Montpellier's Benoît Paillaugue land three penalties apiece, with Remy Tales drop goal for Castres the only difference between the sides.
But a yellow card at the end of the first half for Montepellier's Mamuka Gorgodze proved critical, with Castres pressing their advantage early in the second half until Claassen crossed over for what would be the only try of the match.
Kockott added the extra points and two more penalties, and while another penalty from Paillaugue gave the visitors hope they could get no closer.
Montpellier will play Castres at Stade de la Beaujoire, Nantes, the day after Toulon play Toulouse in the other semi-final, with the winners of those two matches to meat at Stade de France on June 1.
- Sports & Recreation
- Rory Kockott
- Mamuka Gorgodze