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.
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.
Bayonne condemned fellow strugglers Lyon to relegation with a 20-19 away win. in a clash opposing the league's bottom two sides.