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.
Leaders Paris St German have six points more but have still to play this weekend as they host Nice on Sunday.
OM, who occupy the last Champions League direct qualifying spot, lead third-placed Lyon, who beat champions Montpellier 2-1 away on Friday, by two points.
Brest stay second from bottom on 29 points, three points from safety.
"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.
The first shot in a soporific first half came when Andre-Pierre Gignac sent a long-range attempt way over the bar.
Brest were unable to even approach OM's area in a poor game that seemed barely worthy of Ligue 1.
The hosts, however, went ahead in the 45th minute with their first attempt on goal.
Cheyrou curled a fine free kick that bounced on to Alexis Thebaut's left post and into the net.
Centre back Lucas Mendes, who helped OM keep a clean sheet for the sixth match in a row, headed home from a free kick in the second half but the goal was disallowed for offside.
OM goalkeeper Steve Mandanda, who produced a world class performance in their previous game at Lille, pulled off a brilliant save to deny Kamel Chafni in the 75th minute.
Brest, who had a few opportunities in the closing stages, lived up to their status as having the least effective attack in Ligue 1.
- Sports & Recreation