Benedetti, riding for Bora Hansgrohe, had been dropped on the category one Montoso climb around 35km from home but worked his way back before sprinting to the biggest win of his career.
Polanc then had a long wait to discover how much time the main bunch pre-stage leader Valerio Conte and favourite Primoz Roglic had lost.
He will move on to stage 13 with a four minute seven seconds lead over Roglic with Conti another 44 seconds in arrears.
(Reporting by Martyn Herman; Editing by Toby Davis)
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