Florian Fritz (pictured) scored the only try of the match just before the half-hour mark for the hosts, while France fly-half Lionel Beauxis landed six shots at goal - the last of them coming in the penultimate minute - to give his side a narrow win at the Stade de France.
The victory saw Toulouse go top thanks to Clermont's surprise 15-14 defeat away at Biarritz.
Clermont looked on course for their 17th win of the season as they scored two converted tries in the opening half to earn a 14-6 lead, but Dmitri Yachvili's three unanswered penalties in the second half saw the hosts pull off an unlikely victory.
Brive captain Antoine Claassen's 19th-minute try was the difference between the sides as Jonny Wilkinson's Toulon fell to a 14-9 defeat at Stade Amédée-Domenech, a result which leaves Toulon 11 points adrift in third place in the table.
Montpellier hammered Agen 44-18 to leapfrog Castres - who lost on Friday night - and go into fourth place.
Perpignan thrashed fellow strugglers Bayonne 47-9, while basement club Lyon earned just their fifth win of the season as the beat Bordeaux-Begles 24-13. Lyon remain bottom of the table, though they are now just four points adrift of Bayonne.