Foued Kadir almost opened the scoring for Marseille in the 13th minute but his curled effort flew wide of the target following some neat footwork.
Despite looking comfortable for most of the first period, Bordeaux fell behind two minutes before the break when Gignac beat the offside trap before slotting the ball past Cedric Carrasso.
Bordeaux had the opportunity to level the scores just after the interval but Julien Faubert failed to compose himself in front of goal and fired a deflected effort wide.
Marseille continued to dominate the contest in the second period but were fortunate to not concede an equaliser when Cheick Diabate found space to unleash an effort on goal, but his strike was well saved by Steve Mandanda.
The visitors pushed for a point in the final minutes but Marseille were able to hold on to claim a victory.