Nolan Roux's stoppage-time header was enough to see off Ellie Baup's men at the Grand Stade Lille Metropole after the visitors had dominated for large parts of an entertaining clash.
The result kept the victors hot on the heels of PSG, who visit Evian on Wednesday night.
Monaco are third, two points behind the leaders, after an impressive 3-0 win over Nice in the Allianz Riviera.
Goals from James Rodriguez, Emmanuel Riviere and a late Lucas Ocampos strike sealed all three points for Claudio Ranieri's men, who were without top scorer Radamel Falcao due to a thigh injury.
An eighth successive defeat for Nice left them languishing in 15th in Ligue 1, their worst position since the opening day of the season, and heaped pressure on manager Claude Puel.
In the night's other game, Nantes beat struggling Valenciennes 2-1 at the Stade de la Beaujoire.
Following a poor opening 45 minutes, the game burst into life when Jose Saez sent the visitors into a surprise lead after 52 minutes.
However, VA's lead lasted only seven minutes when Alejandro Bedoya levelled before Filip Djordjevic missed a golden opportunity to claim all three points from the penalty spot.
The Serb's blushes were spared though when Fernando Aristeguieta popped up with the winner with two minutes left.