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Despite Marseille's dominance, Kevin Berigaud opened the scoring for the hosts shortly before half time, collecting a long ball forward from Paul Lasne before firing into the bottom corner from just outside the box.
Gignac and Dimitri Payet both pressed early in the second half as the visitors tried to get back on level terms, but Montpellier's defenders held firm, blocking efforts from both players.
Marseille were caught out on the counter-attack just after the hour mark when Anthony Mounier curled the ball in after a quick break from Berigaud was blocked, leaving Lasne to tap in from close range.
The visitors were back in the game just a few minutes later though, as Brice Dja Djeje picked out Billel Omrani, who blasted the ball in from near the penalty spot just a few minutes after coming off the bench.
The home side continued to look the more likely in the final seconds, with Bryan Dabo having an effort blocked, but Montpellier did not need a third goal to clinch the win.
Despite the defeat, Marseille remain at the top of the table, while the win lifts Montpellier up to eighth.