Grégory Sertic had a right-footed shot from outside the box saved, but Sochaux took the lead as Roy Contout converted from inside the box.
Jussie nearly equalised for the home team but got too much on his shot and saw it fly over the crossbar.
Cheick Diabaté also went close but again, Bordeaux's finishing was wayward.
However, it was 1-1 just after 20 minutes when Henri Saivet converted from the penalty spot after Simon Pouplin's foul.
Jussie then struck before half time to give Bordeaux the lead with a header in the bottom corner.
However, Diabate got his second in the dying minutes to wrap up a comprehensive victory.