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The Belgian raced clear of a strong front group inside the final two kilometres to seize the overall lead.
George Bennett (Jumbo-Visma) and Mikel Landa (Bahrain-McLaren) came home second and third respectively, 18 and 32 seconds adrift of the winner.
"The last kilometre was really hard. I was already going flat out and there was a full headwind, but the wind was the same for everyone and I could hear my gap was increasing," Evenepoel said.
"For sure, without the team, I wouldn’t have achieved this victory. They kept me out of the wind all day and they brought me bottles. It was my job to finish it off, as a thank you to the team."
Evenepoel is expected to fight for the maglia rosa at the rescheduled Giro d’Italia in October, despite it being his maiden Grand Tour as a professional.