An Andre-Pierre Gignac goal three minutes before half-time guided Marseille to victory as they closed to within four points of Ligue 1 leaders Paris St Germain.
Gignac conjured a superb finish from Foued Kadir's ball from the halfway line as Marseille kept up the pressure on PSG.
Victory was just reward for OM, who dominated the match and collected their second successive win to move four points clear of third-placed Lyon.
Elie Baup's side almost took an early lead when Kadir pounced on a poor clearance by the Bordeaux defence with his low left-footed volley skimming the top right-hand corner of the goal with Cedric Carrasso motionless.
The goalkeeper was then called upon as he punched clear Andre Ayew's left-footed drive, before he pushed Gignac's shot at the far post away for a corner.
However, Carrasso could do little about Marseille's goal close to half-time. Kadir threaded a ball through for Gignac who was running towards goal.
He collected the ball, controlled it and beat defender Ludovic Sane before firing a low shot past Carrasso.
Bordeaux had not shown as an attacking force and again they were forced to rely on Carrasso who managed to backpedal and block Kadir's lob on the goalline before the keeper then went down to block Gignac's snapshot.
It was not until the 70th minute that Bordeaux produced a shot of note, Benoit Tremoulinas crossed towards Nicolas Maurice-Belay who controlled the ball and ran at speed towards goal before firing in a powerful effort which Steve Mandanda was equal to.
Henri Saivet then headed narrowly over from Tremoulinas' corner with the keeper beaten.
However, that spelled the end of Bordeaux's resistance and Marseille almost doubled their lead in the 89th minute - but Joey Barton's 20-yard shot went inches wide.