Adil Rami's second-half own goal meant Lille failed to reclaim top spot in Ligue 1 following Marseille's win over Montpellier earlier today.
Moussa Sow's first-half strike put the visitors on course for a result which would have seen them end the day where they started it, at the summit.
But Rami headed Jaroslav Plasil's free-kick into his own goal five minutes after half-time and Bordeaux had chances to go on and win the match thereafter.
Lille made a flying start and Eden Hazard forced the first save of the evening from Cedric Carrasso before the keeper was called into action again in the seventh minute when Rami met Yohan Cabaye's corner.
Hazard's free-kick created the next chance, Franck Beria volleying into the side netting, before Bordeaux finally threatened. Anthony Modeste cut the ball back for Jussie, who beat keeper Mickael Landreau but was thwarted by Rami's goal-line clearance.
Beria headed against the post from close range before Lille finally broke through in the 35th minute from a corner. Mathieu Debuchy's backheel and Rami's flick set up Sow to finish from close range.
The lead lasted until the interval but was soon cancelled out as Plasil delivered the set-piece to the near post and Rami, under pressure from the powerful Michael Ciani, could only divert the ball beyond Landreau and into the net.
And it was the Lille keeper who was to the fore in the remainder of the match, most notably with a superb save to keep out Moussa Maazou's fine effort from the edge of the box.
Landreau also kept out Plasil's free-kick as Lille held on for a point which leaves them trailing OM solely on goal difference.