The likes of Mark Cavendish and Fernando Gaviria did not feature after being caught up crash 500m from the line.
BMC's Australian rider Rohan Dennis took the overall leader's jersey from team mate Greg Van Avermaet.
After suffering with illness in the build-up to the race, forcing him to pull out of the Strade Bianche last weekend, Sagan said he was back at full power.
"The season only starts now. I hope this is not the last victory," the Slovakian said after his first victory of the season. Saturday's stage 171-km stage four ends in Terminillo.
(Reporting by Martyn Herman; Editing by Alison Williams)
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