Both sides looked eager to take control of the match in the early stages, but chances were a rarity, with Yeltsin Tejeda coming closest for Evian with a 25-yard strike which drifted wide of the post.
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Evian's best chance to get back into the game was wasted early in the second half when Daniel Wass somehow managed to miss the target with his header from just a few yards out.
It could have been much more comfortable for Montpellier had they taken their opportunities, as Anthony Mounier missed three separate chances to punish Evian for their defensive mistakes.
The hosts eventually wrapped up the win in the final minute when Jonas Martin led a counter-attack before squaring for Mounier, who ended his own frustration by tapping in to confirm the win.