Cheick Diabate scored the only goal as Bordeaux ended a four-match losing run in Ligue 1 to put the pressure back on struggling Bastia.
It was one-way traffic at the Stade Chaban-Delmas and, after Ludovic Obraniak had struck the crossbar, Diabate grabbed the opener having come off the bench for the start of the second half.
The win lifts Bordeaux one place to ninth, while Bastia remain just three points above the drop zone. History was against the visitors even before the match had kicked off, with Bastia winning just two of their previous 29 Ligue 1 fixtures in Bordeaux.
And Les Girondins threatened from the start as Gregory Sertic floated in a corner which was met by the head of Florian Marange before defender Jeremy Choplin cleared the danger.
Sertic then provided another good ball, this time for Henri Saivet, who hit a low shot which was turned away by goalkeeper Mickael Landreau.
Landreau also punched clear a tremendous volley from Diego Rolan to ensure the scores remained level at the interval.
The introduction of Obraniak and Diabate at the restart swung things in Bordeaux's favour, however.
Obraniak first tested Landreau with a 25-yard drive which was palmed away before smashing a left-footed effort off the crossbar in the 54th minute.
Bastia were hanging on by their fingernails but their resistance was finally broken four minutes later by Diabate, who got on the end of a cross from Fahid Ben Khalfallah before stabbing home from close range.
With the goal on the board, Bordeaux spent the rest of the match trying to increase their lead but Landreau rose to the challenge, beating away strikes from Diabate and Jaroslav Plasil.