Striker Victor Montano scored the only goal just before the half-hour mark, boosting his promoted team's chances of qualifying for European competition next season.
Montpellier have 48 points along with Bordeaux, who are top on goal difference and face Saint-Etienne on Sunday.
Lille enjoyed a 3-1 win at home to second-bottom Boulogne with all the goals coming in the first half including a double by Ludovic Obraniak either side of defender Adil Rami's strike.
Lille stay third with 44 points ahead of Olympique Lyon who are still a point behind them after beating visitors Racing Lens 1-0 with Argentinian Cesar Delgado's second-half strike.
Olympique Marseille won 2-1 at Monaco thanks to a late own goal by defender Nkoulou Ndoubena to reach 42 points and remain fifth with a game in hand over their nearest rivals.
Marseille's Senegalese striker Mamadou Niang had converted a penalty after 37 minutes of a tense game but Monaco's new striker Moussa Maazou equalised just three minutes later.
Monaco captain, Argentine Alejandro Alonso, was sent off in added time for showing dissent towards referee Said Ennjimi.
Struggling Paris Saint-Germain ended their four-game losing streak by holding Nancy to a goalless draw away from home.
