Basa headed home from a corner seconds before the final whistle to cancel out Ludovic Obraniak's first-half opener as Bordeaux conceded a goal in added time for the third time this season.
Bordeaux extended their unbeaten run to nine league games and are in fourth spot on 15 points. Lille occupy 10th spot on 11 points.
Francis Gillot's Bordeaux side trail leaders Marseille, who travel to basement side Troyes on Sunday, by four points.
"This draw tastes like a defeat. We need to be more focused," Bordeaux midfielder Landry Nguemo told BeIN Sport television.
Lille defender Aurelien Chedjou said: "It was not easy but we never gave up."
The game started well for Bordeaux at their Chaban Delmas stadium, with Poland midfielder Obraniak heading home after 18 minutes from a Mariano cross following a sharp counter attack.
Lille increased the pressure in the closing stages before the unmarked Basa sent a powerful header past keeper Cedric Carrasso.
On Saturday second-placed Paris St Germain, who are also unbeaten in Ligue 1, take on promoted Stade Reims at the Parc des Princes.