Cedric Yambere scored the only goal shortly after the hour to hand OM a defeat that left them fourth in the standings with 57 points from 32 games, five points adrift of leaders Paris St Germain who have one game in hand.
PSG and second-placed Olympique Lyonnais, who have 61 points, did not play in Ligue 1 this weekend because the French champions were involved in the League Cup final, which they won with a 4-0 defeat of Bastia on Saturday.
Bordeaux, who last lost to OM at home in 1977, are sixth on 54 points with six games remaining.
"Both teams were close and Marseille had their chances in the first half, when we were saved by a couple of great saves by (Cedric) Carrasso," Bordeaux coach Willy Sagnol told Canal Plus.
"But we played with our hearts."
Marseille had great chances in the first half but Romain Alessandrini's attempt from six yards hit the post after 19 minutes.
Alessandrini was at it again four minutes before the break, but Cedric Carrasso tipped the winger's curled shot onto the post as the hosts struggled to keep the pace.
Marseille, who slumped to a second defeat in succession after losing 3-2 against PSG, were denied a penalty on the stroke of halftime when Alessandrini was charged down by Nicolas Pallois in the box.
Bordeaux went ahead in the 61st minute when Yambere beat Steve Mandanda with a half volley from Henri Saivet's cross.
(Reporting by Julien Pretot, editing by Pritha Sarkar)
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