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The home side started strongly and took the lead after just seven minutes through Romain Hamouma, who finished well to make it 1-0.
Bordeaux got themselves into the game and came close to equalising through Andre Biyogo Poko, but his effort was saved by the goalkeeper.
Ludovic Sane then came close for the visitors, but his header was just scrambled away by the Saint-Etienne defence.
Bordeaux almost scored again just before half time, although Cheick Diabate's header was also cleared.
Bordeaux almost got themselves back into the game on 54 minutes when Diabate's effort rattled the crossbar
Jaroslav Plasil came close for the away side, but once again the goalkeeper was equal to his shot.
Ludovic Obraniak grabbed a late consolation for Bordeaux on 90 minutes, but it was not enough as Saint-Etienne took all three points.