"There are films which make you dream, which make you cry, laugh and think, and there are films which change your life forever. This is one of those films," said jury head Darren Aronofki, saying the decision had been unanimous.
Beating 22 other films to the prize, the stomach-turning movie is the final instalment of Sokurov's cinematic tetralogy on the nature of power, following his acclaimed portraits of Adolf Hitler, Vladimir Lenin and Emperor Hirohito.
Sokurov is the second Russian director ever to win the Golden Lion, after it was awarded to Andrei Zviaguintsev for "The Return" in 2003.
"Making auteur cinema is very difficult these days," the St Petersburg-based director said, adding that he was "very happy to live in a Europe where we can understand each other."
The Silver Lion director award went to China's Cai Shangjun for his revenge tale "People Mountain People Sea", this year's surprise addition to the festival line-up, in which a man ceaselessly hunts down his brother's killer.
The film has been censured in China, revealing as it does the appalling conditions in a Chinese mine.
As expected, best actor went to German-born Irishman Michael Fassbender, who plays an emotionally dysfunctional executive addicted to sex in Steve McQueen's powerful "Shame".
Rising star Fassbender -- of "Inglorious Basterds" and "Hunger" fame -- also appeared in another film in the competition this year, David Cronenberg's "A Dangerous Method," where he played psychoanalyst Carl Jung.
Best actress went to Deanie Yip for her portrayal of an elderly maid in a moving tale of the trials of growing old gracefully, "A Simple Life."
The jury at the world's oldest film festival also included US director Todd Haynes, Finnish Eija-Liisa Ahtila, British David Byrne, Italian Mario Martone and Alba Rohrwacher, and French Andre Techine.
The punted favourites -- Roman Polanski's grotesque comedy of manners "Carnage" and George Clooney's political thriller "The Ides of March" -- went home empty handed, as did Tomas Alfredson's much praised "Tinker, Taylor, Soldier, Spy."
"Terraferma," Emanuele Crialese's tale of fishermen from a tiny Italian island who rescue a group of African refugees from drowning at sea, won the special jury prize for "combining social problems with great storytelling."
The theme of immigration inspired several Italian films in this year's programme, and saw Giudo Lombardi win the prize for best film in a parallel section for "La-bas."
For their tale of the struggle for survival in a post-tsunami Japan, Shota Sometani and Fumi Nikaido won the awards for best young actor and actress in Japanese director Sion Sono's "Himizu," which was based on a manga comic strip.
Best screenplay went to "Alps", Yorgos Lanthimos' a tale of actors who try to help people grieve by playing the role of their recently deceased loved ones.
Robbie Ryan was awarded the prize for best photography for "Wuthering Heights" by Britain's Andrea Arnold, a dark adaptation of the tragic love story between Cathy and Heathcliff in Emily Bronte's well-loved novel.
With no musical score, the film is a visual feast for the senses as it portrays the characters' turmoil through the lashing wind and rain, darkness and harshness of elements up on the Yorkshire moors in northern England.
Twenty-three films competed in all in the Mostra, which saw a host of stars arrive by speed boat for the red carpet in the lagoon city, from Madonna to Gwyneth Paltrow, Kate Winslet, Jude Law and "The Godfather" star Al Pacino.
