Cheyrou curled in a perfect free-kick in the 45th minute to give OM, who have 61 points from 33 games with five to play, their 11th 1-0 victory of the season.
OM, who occupy the last Champions League direct qualifying spot, lead third-placed Olympique Lyon, who beat champions Montpellier 2-1 away on Friday, by two points.
"It's not the first 1-0 win, and not the last, hopefully," OM coach Elie Baup told French TV channel Canal Plus.
Brest coach Corentin Martins tried to see the positives in his side's performance.
"We were well organised, and on the free-kick the ball hits the post, it's what happens to struggling teams," he said. "But the team spirit was good."
Baup's side once again failed to impress at their Stade Velodrome but they were never threatened by Brest, who conceded their sixth successive league defeat.
Brest were unable to even approach OM's area in a poor game that seemed barely worthy of Ligue 1.
Cheyrou curled a fine free-kick that bounced on to Alexis Thebaut's left post and into the net.
