The AG2R-La Mondiale rider attacked on the final climb, a 14.1km effort at an average gradient of 6.2 percent, and never looked back, holding off compatriot Thibaut Pinot (FDJ) who reacted too late.
"I did not expect it, I under-performed in (Saturday's) time trial and I had been struggling since the beginning of the season but now I'm on," Peraud, second overall in last year's Tour de France, told France 3 TV channel.
He finished 15 seconds ahead of Frenchman Pierrick Fedrigo (Bretagne Seche Environnement) with Pinot coming home third, one second further back.
Third overall in last year's Tour, Pinot, who impressed when he took fourth place in the Tirreno-Adriatico stage race this month, had targeted victory in the Corsican two-day race.
The FDJ rider let Peraud jump away as he started the day 12 seconds ahead of his compatriot and looked to limit the damage in the closing stages but came up too short to finish second overall with Italian Fabio Felline (Trek Factory Racing) in third.
(Reporting by Julien Pretot; Editing by Ed Osmond)
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