The opening 15 minutes were fairly even with both sides having efforts on goal. Kevin Berigaud missed the target for Evian, while Marseille's Andre-Pierre Gignac found an alert defence in his way as he shaped to shoot.
However, Gignac did open the scoring on 16 minutes. The striker picked the ball up from Rod Fanni and placed it in the bottom corner of the net.
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Evian had further chances as the half wore on, but Cedric Barbosa's shot was blocked and Beriguad fired wide when well-placed.
Shortly after 50 minutes, Payet had another effort but his header missed the target.
Evian's Facundo Bertoglio followed the pattern of missed shots and this was to cost them 20 minutes from the end, as Payet struck from a Mathieu Valbuena assist.
Modou Sougou had two good chances for Evian soon after but failed to hit the target with both.
They continued to press and almost got one back in injury time, but Beriguad struck wide of the post.