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Brive then fought back through a Scott Speeding try which was converted by full-back Julien Caminati to take a 7-3 half-time lead.
It was the second forty minutes which saw all the action with Alexis Palisson collecting a 15-point haul including a try of his own.
Jean-Philippe Bonrepaux crossed for the first try of the second half before a Jonathan Elgoyhen brace, either side of Alix Popham's touchdown.
Fabrice Estebanez and Mathias Atayi rounded up the scoring for the hosts.
Former winners of the tournament Sale Sharks did all they could do in order to keep their European hopes alive by beating Italian side Petrarca 54-0 but Brive's victory at the Stade Pelouse Amedee-Domenech ended their run in the tournament.
The Sharks impressed on Friday evening as they ran in eight tries at Edgeley Park to secure a comfortable bonus-point.
Fly-half Rob Miller ran the show for Sale, scored 19 points including seven conversions and a try, as well as playing a hand in four more.
Chris Brightwell put Sale on track for an emphatic win with the opening try on 11 minutes. Neil McMillan, Miller and Nick Macleod all followed to wrap up a bonus point before half-time.
Prop Henry Thomas resumed the scoring after the break on 44 minutes before Will Cliff, Matthew Tait and John Kennedy all crossed to complete the rout.
Pool 3 leaders Montpellier made it four wins out of five as they took 6 - 0 victory in a tight game at Kingston Park.
The home side are now out of the running for a place in the knock-out stages after suffering their third defeat in the competition but Alan Tait's side can take some credit for their performance on the night.
Newcastle made a number of changes to their side and their squad pushed the high-flying French outfit, third in the Top 14, all the way in a closely-fought contest.
Two penalties in the first half by Benoit Paillaugue was all that separated the teams.
If Exeter Chiefs can beat Bourgoin at home this weekend the Pool will come down to a decider between the English side and Montpellier at Stade Yves du Manoir next weekend.
