Lyon stayed third with 60 points and lead fourth-placed Paris Saint-Germain by two points with two matches left, but PSG have a game in hand at Girondins Bordeaux on Wednesday.
In Ligue 1, the third-placed team is awarded a Champions League qualifying third round spot, while the top two sides automatically qualify for the group stage of Europe's elite club competition.
Lyon trail second-placed Olympique Marseille by six points.
Following a 4-0 thrashing at AJ Auxerre last week, Claude Puel's side played solidly but Mario Licka's superb strike in the second half cancelled out Ederson's first-half opener.
Lyon went in front after 15 minutes when Brazilian midfielder Ederson connected with a Miralem Pjanic corner to beat Steeve Elana from close range.
Kim Kallstrom then blew a clear chance to double the visitors' tally. The Sweden midfielder benefited from a bad clearance by the Brest defence, but his low shot shaved the post as the hosts struggled to approach Hugo Lloris's goal.
As Lyon seemed en route to a routine win, Czech midfielder Licka, who had just come off the bench, fired a volley into the top corner from a Nolan Roux cross in the 76th minute.
Brest are 15th in the standings with 43 points, two above safety.
