The Astana rider, who has struggled througout the season and was thrown out of the Vuelta a España last month for holding onto a team car, attacked on the penultimate descent and never looked back.
Dani Moreno (Katusha) and 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 to Como.
"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.
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 one of the best descenders in the world.
"I can't explain how I descend the way I do, Nibali said. "You either have it or you don't, I think, although, as a descender, Sagan is even crazier than I am. At least I try to keep a margin for error.
"Everyone knew that I wanted a result today, which meant that I was very closely marked on the way up the Civiglio.
"We all had the same number of kilometres in our legs, and it wasn't easy to invent a race-winning move, but I managed to come up with something at the top of the descent.
"I was kept constantly aware of what was happening behind me. I built a good lead and I knew the reaction from the chasing group would be strong, but I rode at a very even pace and, once I reached at the top of San Fermo, the ride into Como seemed to go by in a moment."
Pinot and Moreno were stronger than the rest of the top of the final climb but failed to close the gap.
"My team-mates were exceptional, starting with (Alessandro) Vanotti and (Valerio) Agnoli early on, all the way to (Mikel) Landa, who was brilliant, and (Diego) Rosa, who was still strong in the closing kilometres. It was not easy, but we did not relent all race, and I am truly happy now."
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