The victory puts Toulouse level with Clermont on 82 points at the top of the table with two matches remaining, meaning they will both avoid having to contest a play-off for one of the two other semi spots.
Toulouse, who suffered two straight defeats going into the match, looked nervous in the early stages and Brive opened the scoring with a sixth-minute penalty.
But the host struck back with tries from Clement Poitrenaud and Julian Clerc, the latter of whom was making his first appearance in five weeks after injuring his shoulder.
The visitors responded with a try from Jacques Boussuge and led 18-15 at half-time, but after the break Luke McAlister kicked five penalties to seal the win for Toulouse.
Argentina prop Rodrigo Roncero scored a try for the Parisiens on his final home league game for the club, while George Smith added a second, but it was the boot of Julian Dupuy which won Stade the match as he kicked 25 points in total.