The hosts' Youssouf Sabaly was the first to create the game's opening chance when he saw his right-footed shot from the left side of the box saved in the bottom left corner of the Bastia goal.
Bastia's lead was not to last long, though, as Evian replied in the 35th minute through Benezet, who collected Kevin Berigaud's pass to slot home from the centre of the box.
The hosts turned the game around in the second half as they took the lead, thanks to a free kick from Wass, which saw him crash the set piece into the bottom corner.
Cisse almost grabbed an equaliser in the 61st minute when he was picked out by Ryad Boudebouz's cross, but the striker couldn't keep his header down.
Boudebouz then sought to take matters into his own hands with an effort from distance, but Jesper Hansen was equal to it as Evian held out to claim the win.