The film, which stars Oscar winner Mahershala Ali and Viggo Mortenson, is set in the Sixites. It tells the story of a black classical musician and the driver who takes him on a tour of the Deep South.
The festival prize is seen as marking out films to watch in awards season, with every winner of the accolade since 2012 going on to be nominated for an Oscar. Previous winners of the Academy for Best Film and the Toronto prize include The King's Speech and Slumdog Millionaire.
The second prize went to Barry Jenkins' adaptation of James Baldwin's If Beale Street Could Talk, about a woman striving to prove her fiance's innocence.
Third prize went to Alfonso Cuarón's semi-autobiographical Roma - which will screen at San Sebastian,