The visitors took the lead in the 17th minute when Nicolas Pallois rose highest in the penalty area to head an effort past Marc Vidal.
Bordeaux doubled their advantage minutes later when they hit Toulouse on the counter-attack, and Diego Contento slotted the ball past Vidal with a neat finish.
Toulouse tried to hit back before the break, but the visitors' backline proved to be resolute as they thwarted the home side's attempts to get themselves back in the match.
In the second half, Bordeaux were reduced to 10 men when Pallois was sent off for his second bookable offence after he brought down Ben Yedder with a poor challenge.
However, the loss of a man didn't deter Willy Sagnol's side from pushing forward, and they all but sealed the result when Cheick Diabate scored their third goal of the match, as he curled an effort into the bottom corner.
Toulouse got a consolation goal late on when Jean Daniel Akpa found the net, but the visitors held out to advance to the next round.