PSG consolidated its lead atop the league by routing Lorient 4-0 on Friday.
Monaco playmaker Joao Moutinho created the first chance after five minutes with a drive from the edge of the box that was punched away by Lille goalkeeper Vincent Enyeama.
The hosts then capitalized on a corner to open the scoring in the 27th when Lille center back Marko Basa outjumped the Monaco defense to win a header that Roux flicked home.
Lille defender Simon Kjaer nearly put his team in trouble with a weak backpass in the 36th but Enyeama came off his line to beat Monaco winger Yannick Ferreira Carrasco to the ball and clear the danger. Radamel Falcao pounced on the loose ball but the Monaco striker could only shoot over the bar despite an empty net.
Roux nearly added a second goal on the stroke of halftime but Monaco goalkeeper Danijel Subasic palmed away the cross-shot from the Lille striker.
Monaco coach Claudio Ranieri added more firepower by replacing Carrasco with forward Emmanuel Riviere in the 46th.
"We had a poor first half," Riviere said. "Then we had chances to rally. Unfortunately their keeper made great saves."
Riviere collected a through ball from James Rodriguez to be clean through on goal in the 67th but was denied by Enyeama. The Monaco goalkeeper protected his team's lead by stopping a powerful strike from Falcao in the 71st.
A few seconds later, Salomon Kalou punished Monaco's attempts to push forward by leading a counterattack. Kalou released Mavuba down the left wing and the Lille captain made a low cross for Roux, who tapped in.
Enyeama showed his class in stoppage time with a double save, first parrying an angled strike from Falcao before stretching on the ground to prevent Riviere from converting the rebound.
Monaco dropped to third, one point behind Lille.
Meanwhile, Serbian striker Filip Djordjevic put Nantes ahead in the 22nd minute with his seventh goal this season, diverting in a shot from his teammate Issa Cissokho.
But Montpellier substitute Djamel Bakar equalized with a low strike into the bottom corner in the 90th.
"Although we opened the scoring, Montpellier imposed its game," Nantes coach Michel Der Zakarian said. "Our ball retention was poor and they were stronger in duels."
Montpellier ended a three-match losing streak but slipped to 16th place.
"A draw is still better than nothing," Montpellier coach Jean Fernandez said. "But we can be disappointed tonight because we did everything in the second half to come away with the three points."
At the Allianz Riviera stadium, Bordeaux midfielder Gregory Sertic fired into the top corner from 25 yards in the 31st, and Ludovic Obraniak doubled the lead with another long-range strike in the 59th.
Argentine striker Dario Cvitanich scored his seventh goal this season with a penalty after Bordeaux defender Lucas Orban had fouled Alexy Bosetti in the 77th.
Bordeaux moved into the middle of the table, level on points with Nice.
"We stuck together in hard times," Bordeaux midfielder Ludovic Obraniak said. "We knew we had a quality squad but we were making positional mistakes."
Bordeaux is usually a contender for a European spot but it got off to a poor start this season.
"We played poorly in the first half," Nice coach Claude Puel said. "Bordeaux pressed high up the pitch and we were not able to adjust. We lost confidence little by little."
