A late attack saw Woods (EF Education First) surge clear of 2018 world champion Valverde (Movistar) in the final kilometre to cross the line in 4:03:48.
Briton Yates was five seconds behind and completed the podium fresh off the Mitchelton-Scott rider's overall victory at the Tour of Croatia.
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Tour de France champion Egan Bernal (Ineos) finished sixth behind Tiesj Benoot and David Gaudu.

'What a battle' - Woods takes Milan-Torino victory

The one-day race falls in the week building up to Il Lombardia on Saturday - the last Monument of the season - which is live on Eurosport and the Eurosport Player.
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