Neither side was able to carve out a clear goalscoring chance of note during the opening 45 minutes as both defences were on top.
However, the home side went close to breaking the deadlock just three minutes after the restart. Younes Belhanda swung over a corner for Souleymane Camara, who guided a headed effort just wide of the target.
The winning goal arrived with 13 minutes of the match remaining. Montpellier defender Daniel Congre presented the ball to Marseille's Morgan Amalfitano, who in turn threaded a pass to Gignac. The striker evaded his marker, before beating Geoffrey Jourdren at his near post.
The defeat has seen the champions fall into the Ligue 1 relegation zone.