Substitute Zouheir Dhaouadi scored the only goal of the game with 10 minutes to play as Evian took all three points away from Rennes.
Both defences started the game solidly with Rennes the most threatening side, as evidenced by a series of corners inside the opening 20 minutes.
However it was Evian who came closest to scoring on 23 minutes when Fabrice Ehret beat the goalkeeper but struck the face of the crossbar.
Five minutes later Romain Alessandrini managed to hit the target for Rennes, but he did not do enough to beat Bertrand Laquait in the Evian goal.
In the 58th minute Allessandrini again tested Laquait but the visiting goalkeeper was solid again.
Dhaouadi came on in the 75th minute and in the 80th he broke the deadlock after being set up by Brice Dja Djedje.
Rennes were unable to find a goal in the final 10 minutes and Evian took the points.
