Midfielder Cheyrou controlled the ball on his chest and volleyed home nine minutes from time to allow the visitors to share the points with the champions, now seven points clear of second-placed Lille who beat Paris St Germain 3-1 on Saturday.
Bordeaux, who had defender Marc Planus sent off for a dangerous tackle in the second half, moved in front with a controversial own goal just before half-time, Marseille keeper Steve Mandanda sending the ball into his net under pressure from Marouane Chamakh.
The Marseille players protested that the Morocco striker had pushed Mandanda and television replays suggested he had but referee Laurent Duhamel ruled the goal was valid.
Bordeaux moved on 44 points from 20 games with Lille, who have won their last seven matches by scoring at least three goals in each, second on 37.
Marseille remained fourth, 11 points off the pace and three behind third-placed Montpellier who beat Nice 1-0 on Saturday.
"It's a real shame and it's difficult to swallow," said Marseille coach Didier Deschamps, who blamed the match officials for awarding the Bordeaux goal.
"A point is a good result but we could have won and some decided we wouldn't," Deschamps told French television channel Canal Plus.
Bordeaux suffered after the break when goalkeeper Cedric Carrasso had to be substituted with an injury before Planus receiving his marching orders on the hour for a challenge on Marseille captain Mamadou Niang.
Marseille stepped up a gear and came close to scoring shortly before equalising, Bordeaux defender Benoit Tremoulinas clearing a Niang header off the line.
