English forward Stephy Mavididi found the back of the net for the hosts early in the second half to lift his team up to 13th on 13 points from 10 games.
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Lens have 18 points and trail PSG by nine points. But they are now in danger of being overtaken by third-placed Nice, who are two points behind following a 1-0 defeat at Troyes but have a game in hand.
Montpellier started well and came close to opening the scoring in the eighth minute when Valere Germain's strike crashed onto Jean-Louis Leca's post.
The visitors piled on the pressure but could not play their usual eye-pleasing quick passing game and failed to really threaten.
Montpellier were close to doubling the advantage but Leca parried another Germain attempt in the 64th.