Lille came into the game having won five of their last six games, but it was the away side who started the contest the brighter, as Vincent Enyeama had to stretch to push Gregory Sertic's fourth-minute free kick away.
The Nigerian goalkeeper, who came into the contest having not conceded a goal in more than 1,000 minutes, then tipped Landry N'Guemo's volley over the bar, but the Cameroonian got the better of Enyeama two minutes later.
The midfielder fired a shot towards goal, which deflected beyond the reach of the goalkeeper to give Bordeaux a 1-0 half-time lead.
However, Maxime Poundje was shown a straight red card for the hosts just before the hour mark as Lille began to see more of the ball.
Bordeaux were content to sit behind the ball, though, and Lille found it difficult to break down the defence.
Indeed it was the home team who had the match's next chance, as Sertic sliced his effort wide following an incisive counter-attack.
WIth five minutes remaining, the Bordeaux goalscorer N'Guemo reacted quickly to block a Lille header on the line as the hosts secured all three points to edge closer to fourth place.