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.
The win, however, was not enough for coach Laurent Blanc as Bordeaux travel to Juventus on Tuesday in their opening Champions League game.
"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.
Olympique Marseille, who will also be in Champions League action against AC Milan on Tuesday, did not have it all their way at Le Mans but they won 2-1 with a superb Brandao display.
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."
Marseille, fourth in the standings, are one of six unbeaten teams as are third-placed Montpellier who beat fellow newly promoted RC Lens 1-0 at home.
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