Vermut, 34, also took the best director prize for the movie, his second feature film, at a glittering ceremony in the northern Spanish seaside resort of San Sebastian late on Saturday.
"It is an honour and a privilege for us," he said as he collected the prizes at the ceremony.
Danish actress Paprika Steen was given the best actress award for her role as the daughter of a terminally-ill woman in "Silent Heart", directed by fellow Dane Bille August.
The movie had its world premier at the San Sebastian Film Festival, the oldest and most prestigious event of its kind in the Spanish-speaking world.
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Spanish actor Javier Gutierrez won the best actor award for his interpretation of a policeman in thriller "Marshland" about the search for a serial killer.
The festival also presented special lifetime achievement awards to Oscar-winning US actor Denzel Washington and Benicio del Toro, who paid homage to his native Puerto Rico as he picked up the prize.
"I want to dedicate this award to the piece of land where I come from, where I was born, where I learned to throw rocks and had them first thrown at me," he said at the award ceremony.
"Where I learned to take risks and where I learned not to do things just to do them."
The Donostia Award -- the Basque name for the coastal city San Sebastian -- has been given out each year at the festival since 1986 to "a great film personality in recognition for their work and career."
Past recipients include Gregory Peck, Bette Davis, Susan Sarandon, Meryl Streep, Richard Gere and Robert De Niro.