Peters jumped away from a group of breakaway riders and the AG2R-La Mondiale rider held off the chasers in the final climb, a 5.5-km effort at an average gradient of 6.9%.
Colombian Esteban Chaves finished second ahead of Italian Davide Formolo.
Ecuador's Richard Carapaz retained the overall leader's pink jersey, extending his lead over second-placed Vincenzo Nibali by seven seconds to 1:54 after a late attack.
Slovenian Primoz Roglic also lost seven seconds and sits in third place overall, 2:16 off the pace.
Spain's Mikel Landa, Carapaz's teammate, launched an attack midway through the final ascent for the gain of 19 seconds on Nibali and Roglic as Movistar hope to place two riders on the final podium in Verona on Sunday.
(Writing by Julien Pretot; Editing by Christian Radnedge)
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