The French champions are ahead of Montpellier on goal difference with both teams on 52 points, two clear of Olympique Lyon.
The match turned sour for Bordeaux on the half hour when defender Michael Ciani was handed a straight red card for a foul on Colombian striker Victor Hugo Montano.
Alberto Costa took the resulting penalty but Cedric Carrasso denied him with a spectacular dive to his left.
The second penalty came four minutes before the break when Matthieu Chalme handled the ball in area.
Montano took the penalty this time and had his first effort disallowed by the referee. At the second attempt, Bordeaux keeper Carrasso once again dived to his left and saved it.
Bordeaux scored on the hour when Marouane Chamakh controlled the ball after a long-range free-kick and netted with a powerful right foot shot.
Montpellier levelled four minutes into added time when Costa redeemed himself with a 30-metre free-kick.
Olympique Marseille failed to put any pressure on the top two when they were held to a 1-1 draw at home by mid-table Lorient.
After missing several chances, Marseille seemed to have done the hard work when Ligue 1 top scorer Mamadou Niang recorded his 15th goal of the season just before half time, banging in a cross from Laurent Bonnart.
Laurent Koscielny, however, levelled in the 64th minute with a scrappy goal.
The 25-year-old defender caught a Marama Vahirua free-kick with the back of his head, Marseille goalkeeper Steve Mandanda deflected the ball on to the post but Koscielny recovered it and pushed it over the line.
Marseille pushed hard until the final whistle but Lorient goalkeeper Fabien Audiard denied each of their attempts.
"Of course, I'm disappointed. We had 12 chances and failed to score a goal but we still have along way to go before the end of the season," Marseille coach Didier Deschamps told a news conference.
Marseille stay fourth in the table on 49 points.
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