Bordeaux's woes were compounded when defender Pablo was shown a red card two minutes from time for a poor tackle on winger Nicolas Pepe.
Victory took Lille to 72 points with two games to go. Lyon, on 63 points and with a game in hand, take on Olympique de Marseille in Sunday's late game.
Champions Paris St Germain last month secured an eighth league title and their sixth in seven seasons.
The top two in Ligue 1 are guaranteed automatic Champions League berths while the third-placed team will enter the elite club competition's qualifying rounds.
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Tony Lawrence)
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