Gouffran was perfectly set up just inside the box by fellow midfielder Jaroslav Plasil before slotting the ball past keeper Jody Viviani in the 18th minute.
Bordeaux, with 13 points from five matches, lead on goal difference from Olympique Lyon, who beat Lorient 1-0 with a Michel Bastos goal earlier on Saturday.
"I don't mean to be picky but we will have to play much better if we want to hope for anything in Turin," he told French TV channel Orange Sport.
The Brazilian striker set up Senegal's Mamadou Niang for a splendid volley in the 14th minute and sealed the win with a timely header 21 minutes from time after the hosts had levelled through Modibo Maiga just after the hour.
"We did not make it easy for ourselves," Marseille coach Didier Deschamps told reporters.
"We had the situation under control in the first half but we did too many complicated things after that and missed our chances for 2-0."
