Roux scored his sixth goal this season by heading a cross from Florent Balmont into the bottom corner in the first minute of stoppage time, while Lille goalkeeper Vincent Enyeama kept an 11th straight clean sheet in the league.
Lille pulled within a point of PSG and is nine points clear of Marseille.
”I’m sorry for those who will say: again a 1-0 victory,” Lille coach Rene Girard said. ”Football is about defending and attacking. We did attack since we scored a goal. We’re efficient. We don’t dominate by creating 20 chances per game. But we step up when it matters.”
Florian Thauvin was booed by the crowd at Stade Pierre Mauroy every time he touched the ball. The Marseille forward went on strike this summer to obtain a transfer from his former club, Lille.
Lille tested Marseille goalkeeper Steve Mandanda with long-range strikes from Ronny Rodelin in the fifth minute and Balmont in the 14th.
But Andre-Pierre Gignac was the most threatening player in the first half, forcing Enyeama to punch away his cross-shot in the 17th. The Marseille striker then rolled away from Lille defender Simon Kjaer to be clean through on goal in the 24th, but Enyeama denied him.
The Lille goalkeeper frustrated the visitors in the second half, stopping a close-range effort from Gignac in the 54th, a drive from Thauvin and a volley from Gignac in the 63rd.
Marseille lost France playmaker Mathieu Valbuena and Dimitri Payet to injuries in the 72nd and the 78th, respectively.
Meanwhile, substitute Fernando Aristeguieta volleyed home a corner in the 89th to give Nantes a 2-1 win over Valenciennes.
Jose Saez gave Valenciennes the lead with a lob in the 52nd. But Nantes forward Alejandro Bedoya levelled with a long-range strike that deflected off defender Benjamin Angoua in the 59th.
Valenciennes goalkeeper Nicolas Penneteau saved a penalty from Filip Djordjevic in the 72nd after the Nantes striker was fouled by Angoua.
Monaco played Nice later Tuesday.
On Wednesday, it’s: Evian vs. Paris Saint-Germain; Rennes vs. Saint-Etienne; Guingamp vs. Bordeaux; Ajaccio vs. Bastia; Sochaux vs. Reims; and Montpellier vs. Lorient.