Gianelli Imbula fired an early shot wide for the hosts, but they were soon behind when Mounier received a pass from Abdelhamid El Kaoutari on the left side of the area and fizzed an effort across goal into the corner.
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Marseille came close to an equaliser before half time, but the game was then put out of reach midway through the second period.
Mounier turned provider, crossing to Sanson, who couldn't miss from inside the six-yard box.
Victory sees Montpellier climb up to 10th in the early table, while Marseille are still winless in 16th.