Second-half goals from Cedric Barbosa and Daniel Wass lifted Evian five points clear of 18th-placed Valenciennes, who play on Saturday.
It was the hosts who did the early pressing, with Tulio de Melo heading wide of the right-hand post from a Barbosa cross in the opening stages.
Alejandro Bedoya rattled the crossbar for Nantes with a headed effort in the 23rd minute, but the rebound bounced favourably for Evian to clear the danger.
Nantes had claims for a penalty turned down on the half-hour mark when Cedric Mongongu was alleged to have brought down Johan Audel, who was eventually brought off injured.
Evian then broke the deadlock in the 61st minute, when Barbosa watched the ball float over his shoulder from a delightful Olivier Sorlin pass and allowed it to bounce before powering home a left-footed effort from close range.
The points were secured 16 minutes later when Wass curled home a superb set-piece from 20 yards, although questions were raised over whether a free-kick should have been awarded in the first place.
Nantes could have had a penalty in stoppage time, when Itay Shechter appeared to be felled by Mongongu in the area, but the referee awarded a corner instead.
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