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It was sixth seeded Schwartzman's first tournament win on the ATP world circuit since Istanbul's clay championship in 2016.
The 25-year-old, one of the shortest players on the tour at 1.75m (5ft 7ins) bettered his veteran rival Verdasco, 34, and jumped in the rankings from 23 to 18 -- his first taste of the top 20.
Verdasco, seeded eighth, had been hoping to get his first title since Bucharest in 2016 but was let down by errors throughout the match.