Four-time Tour de France winner Pogacar attacked with 22km remaining of the 298km one-day Monument, and only Pidcock and Mathieu van der Poel were able to follow him.
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Two-time winner Van der Poel fell on the final climb, the Poggio, leaving Pogacar and Pidcock to compete in the final.
Pogacar launched his sprint first and Pidcock battled to get alongside but was overtaken as they both lunged for the line.
The Slovenian, already considered one of the best cyclists of all time, has won four of the five ‘Monuments’ (the most prestigious one-day races in men’s cycling) with only Paris-Roubaix remaining.
Saturday’s victory puts him level with Roger de Vlaeminck for second place on the list of most wins at the Monument, with 11. Only the legendary Eddy Merckx has more, with 19.
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The 27-year-old’s victory was even more notable given that he recovered from a crash just before the key Cipressa climb to return to the main group.
“For a second I thought it was over, but luckily I quickly got back on the bike,” he said.
“Pidcock was really strong. I was lucky in the sprint, he’s a very fast guy.”
Like Merckx, Pogacar is a rare rider capable of winning three-week Grand Tours and one-day races.
Merckx won 11 Grand Tours, 19 Monuments and three world road titles. Pogacar has five, 11 and two respectively, but, with no signs of his dominance fading, he is firmly in contention to be considered the greatest of all time.
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That Pinarello-Q36.5’s Pidcock was the only man capable of matching the UAE Team Emirates-XRG driver was very impressive, especially when even Van der Poel, winner of two of the last three editions, fell apart.
The double Olympic mountain bike champion, 26, came into the race in form, having won Milan-Torino on Wednesday, and was looking to become the third British cyclist to win the famous race after Tom Simpson and Mark Cavendish.
In the end, only an all-time great could deny him, although his performance here, full of wit and technical skill to stay with Pogacar on the descent of the Poggio, suggests he will be a threat in the monuments to come.
Wout van Aert, the 2020 winner, pulled away from the chasing group late to finish third.
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Belgian Lotte Kopecky won the previous women’s race, during which Italian Debora Silvestri was taken to hospital after a serious accident.
Men’s Milan-San Remo results
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Tadej Pogacar (Slo/UAE Team Emirates-XRG) 6h 35m 49s
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Tom Pidcock (GB/Pinarello-Q36.5) Same time
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Wout Van Aert (Bel/Visma-Lease a Bike) +4 seconds
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Mads Pedersen (Den/Lidl-Trek) Same schedule
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Andrea Vendrame (Ita/Jayco-AlUla)
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Jasper Stuyven (Bel/Soudal-QuickStep)
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Mathieu van der Poel (Ned/Alpecin-Premier Tech)
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Matteo Trentin (Ita/Tudor)
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Edoardo Zambanini (Ita/Bahrain victorious)