Dimitri Yachvili kicked 14 points and Damien Traille crossed for the game's only try as Biarritz set up a May 18 clash with Toulon in the final, after they were 32-29 winners over Stade Francais on Friday.
Yachvili missed an early penalty but kicked his next two to put Biarritz 6-0 up after the opening quarter of the game, Riaan Swanepoel missing for Brive in between times.
And good work by Marcelo Bosch sent Traille over for the game's only touchdown, which was awarded after consultation with the television match official. France team-mate Yachvili added the extras to make it 13-0 at half-time.
Brive had another chance to pull back three points in the 48th minute but Swanepoel was off-target again.
That was the end of the scoring, and the game finished on a sour note for Brive when Alexandre Barozzi was red-carded in the last minute.