The Astana rider, who was thrown out of the Vuelta last month for holding onto a team car, attacked on the penultimate descent and never looked back.
Spain's Dani Moreno (Katusha) and Frenchman Thibaut Pinot (FDJ), who jumped away from the group of favourites in the last climb to lead the chase, finished second and third, 21 and 32 seconds back respectively after 245km from Bergamo.
"It was a fantastic day, the whole team worked very well," said Nibali, who was sheltered by Diego Rosa in the last part of the race, one of five 'Monument' classics with Milan-San Remo, the Tour of Flanders, Paris-Roubaix and Liege-Bastogne-Liege.
Nibali's best results in the Monuments so far had been third place on Milan-San Remo and second in Liege-Bastogne-Liege in 2012.
"I tried to attack on the climb but I realised I had to do it differently," he added.
Nibali attacked in the ascent of the Civiglio but he was reined in by Pinot. He attacked again in the downhill and no rider was able to follow the Italian, one of the best descenders in the world.
Pinot and Moreno were stronger than the rest of the top riders in the final climb but they failed to close the gap, which rose again a little bit in the last downhill part of the race.
(Writing by Julien Pretot; Editing by Alan Baldwin)
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