Les Verts stayed in fourth place on 59 points with three games left, one point behind arch-rivals Olympique Lyon, who visit relegation-threatened Nancy on Sunday.
The top two teams in Ligue 1 qualify directly for the Champions League group stage while the third-placed side go into the third qualifying round.
St Etienne dominated Friday's match with their Gabon striker Pierre-Emerick Aubameyang again missing several chances in a lively game at the Geoffroy Guichard stadium.
Bordeaux's defence held firm under pressure and the visitors' only chance came in the 73rd minute when Julien Faubert's 20-metre strike went over Stephane Ruffier's bar.
Bordeaux remain eighth on 49 points.
On Saturday, second-placed Olympique Marseille host Bastia knowing a win will delay Paris St Germain's capture of the title with the league leaders hosting Valenciennes on Sunday.
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