Brest took an early lead when Kamel Chafni struck past the goalkeeper after just eight minutes.
Alexandre Lacazette came close to bringing the away side level on 12 minutes, but his effort was blocked well by a determined defence.
Bafetimbi Gomis had another effort for Lyon, but he put his shot wide of the post as his side began to push forward.
The home side continued to look dangerous when coming forward, with Mario Licka and Chafni both having shots on goals towards the end of the first half.
Lyon drew level on 53 minutes through a Tripy Makonda own goal after some early pressure in the second half.
Remi Garde's side went in search for a winner with Gomis and Steed Malbranque both having efforts on goal, but neither could find the finish.
Gomis broke free again in injury time, but he could only hit his shot wide of the mark as the referee blew the final whistle.