Bordeaux were already certain of losing their Ligue 1 crown after they had lost five and drawn one of their previous six league games.
An early header by defender Michael Ciani helped them move up to fifth place on 60 points, four behind Lille with three games left and ahead of Montpellier on goal difference.
Montpellier suffered a 1-0 home defeat to Olympique Lyon, who climbed to fourth two points behind Lille with a game in hand.
Third-placed Lille hold the only Champions League preliminary-round qualification spot in Ligue 1 after they beat Nancy 3-1 at home.
"The most important thing tonight was to win, no matter how. That's what we needed to get a boost," Ciani told Foot Plus TV channel. "It helps us believe we can end the season in the top three."
Olympique Marseille moved closer to their first Ligue 1 crown in 18 years when they drew 0-0 at second-placed Auxerre on Friday. Marseille lead the table on 72 points, five ahead of Auxerre.
CHAMPIONS STRUGGLE
Bordeaux got off to a good start and Ciani headed home the winner from a Wendel corner kick in the 17th minute. The champions struggled thereafter as they seemed to fear yet another setback.
"It's been a long time since Bordeaux's last win and you can see tonight how hard we had to work to get another one...We're happy but exhausted," Bordeaux coach Laurent Blanc told reporters.
In Montpellier, Olympique Lyon created the best chances in first half but Argentine striker Lisandro Lopez first hit the post in the 15th minute before shooting wide from inside the box minutes later.
Montpellier pushed hard on Lyon's goal after the interval but were left trailing against the run of play when defenders Mapou Yangambiwa and Abdelhamid El Kaoutari collided and let Michel Bastos run towards the goal to fire home the winner with less than 20 minutes to play.
"We were a bit nervous as we knew the results of our rivals. We had to be strong and we were although we can play better... we're going to play Auxerre, who has been rested since Friday," Lyon coach Claude Puel told Canal Plus, in a reference to his side's next game at home on Wednesday.
Second from bottom Boulogne kept a slight hope of escaping relegation when three goals in the last 10 minutes helped them snatch a 3-3 draw at home against Nice.
The Northern side are on 28 points, eight behind St Etienne, the last club above the drop zone whom they will host on Wednesday.
St Etienne squandered an opportunity to seal Boulogne and Le Mans' fates as they suffered an embarrassing 4-1 home defeat by Racing Lens after having opened the scoring in the first half.
Le Mans, who drew 1-1 at Monaco on Tuesday, have 29 points.
