Colombian climber Quintana, 22, took his seventh win of the season by three seconds from Fredrik Kessiakoff of Astana on the finishing San Luca climb of the Italian classic.
Franco Pellizotti (Androni Giocattoli) was third at four seconds ahead of Domenico Pozzovivo (Colnago-CSF Bardiani) and Chris Anker Sørensen (Saxo Bank-Tinkoff Bank).
Quintana attacked with 600 metres remaining to continue Colombia’s recent success in Italian races.
He secured overall triumphs in this year's Vuelta a Murcia and Route du Sud and stage wins in those races as well as stage six of the Critérium du Dauphiné.
He helped Movistar to the stage one team time trial at the Vuelta a Espana.