Brive clung on for a one-point win in Saturday's late game in the Top 14, securing a 19-18 victory to move up to fifth in the table ahead of Sunday's fixtures.
The hosts grabbed the only try of match just after half-time through centre Poutasi Luafutu as scrum-half Teddy Iribaren added 14 points with the boot.
Three penalties from Demetri Catrakilis and another from Benoit Paillaugue gave the visitors a 12-3 advantage in the first half, with Iribaren's second three-pointer just before half-time keeping Brive within range.
Luafutu then struck in the 42nd minute, looping round Matthieu Ugalde into space and having the speed to score.
Iribaren's conversion put Brive ahead at 13-12 and into the lead for the first time.
Another penalty from the scrum-half eased the nerves of those watching on at the Stade Amédée Domenech but Catrakilis responded to once again keep the sides separated by only a score.
Both players traded further penalties to set up a tense finish at 19-18, with Brive replacement Thomas Laranjeira hitting the post.
Montpellier still had one last-gasp attack up their sleeve from within their own 22 but were penalised at the breakdown, Laranjeira booting the ball into touch to secure the win.
Pens: Iribaren 3
Pens: Catrakilis 5, Paillaugue
Brive: 15 Matthieu Ugalde, 14 Guillaume Namy, 13 Arnaud Mignardi, 12 Poutasi Luafutu, 11 Benito Masilevu, 10 Nicolas Bezy, 9 Teddy Iribaren, 8 Sisa Koyamaibole, 7 Dominiko Waqaniburotu, 6 Petrus Hauman, 5 Arnaud Mela, 4 Peet Marais, 3 Giorgi Jgenti, 2 Guillaume Ribes, 1 Karlen Asieshvili.
Replacements: 16 Francois Da ros, 17 Lucas Pointud, 18 Wilhelm Steenkamp, 19 Fabien Sanconnie, 20 William Whetton, 21 Jean baptiste Pejoine, 22 Thomas Laranjeira, 23 Damien Jourdain.
Montpellier: 15 Jesse Mogg. 14 Julien Malzieu, 13 Anthony Tuitavake, 12 Ben Lucas, 11 Marvin O Connor, 10 Demetri Catrakilis, 9 Benoit Paillaugue, 8 Ben Mowen, 7 Willem Liebenberg, 6 Fulgence Ouedraogo, 5 Paul Willemse, 4 Robins Tchale watchou, 3 Jannie du Plessis, 2 Bismarck du Plessis, 1 Mikheil Nariashvili.
Replacements: 16 Charles Geli, 17Jamie Mackintosh, 18 Thibaut Privat, 19 Antoine Battut, 20 Akapusi Qera, 21 Nicholas White, 22 Robert Ebersohn, 23 Davit Kubriashvili.
Referee: Pascal Gauzère