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Yusuf Yazici, Timothy Weah and Jonathan David scored second-half goals as Lille put the pressure back on chasing duo Lyon and Paris Saint-Germain, who play Dijon and Nimes respectively later.
Turkey international Yazici slammed a pass from Jonathan Bamba into the roof of the net on 54 minutes as Lille eventually broke down Bordeaux.
Weah then applied the finishing touch from a Luiz Araujo lay-off as the Brazilian ran free of the Bordeaux defence following a blistering counter-attack just past the hour.
Lille goalkeeper Mike Maignan made a superb reflex save to turn away Hwang Ui-jo's header, and the visitor added a late third through Canadian substitute David.
Fifth-placed Rennes conceded an 83rd-minute equaliser in a 1-1 draw at home to resurgent Lorient, which climbed out of the bottom three having defeated PSG at the weekend.
Metz extended its unbeaten run to six matches following a 1-1 draw with Montpellier, while Brest drew 2-2 at Strasbourg and the game between Reims and Angers finished goalless.