He also won an Oscar in the best foreign language category for his 1999 film "All About My Mother".
Now aged 74, he has decided to try his hand at English, telling reporters that it was like science fiction for him.
Speaking ahead of the premiere, he said his movie highlighted the importance of cherishing life, but also made clear that people should be able to die with dignity at a time of their choosing.
"It's a film in favour of euthanasia," he said, criticising countries such as the United States, where so-called "mercy killing" is illegal, unlike his native Spain.
While "The Room Next Door" had been widely tipped to win, the runner-up Silver Lion award was a surprise, going to Italian director Maura Delpero for her slow-paced drama set in the Italian Alps during World War Two - "Vermiglio".
Australia's Nicole Kidman won the best actress award for her risque role in the erotic "Babygirl", where she plays a hard-nosed CEO, who jeopardises both her career and her family by having a toxic affair with a young, manipulative intern.
Kidman was in Venice on Saturday, but did not attend the awards ceremony after learning that her mother had died unexpectedly.
France's Vincent Lindon was named best actor for "The Quiet Son", a topical, French-language drama about a family torn apart by extreme-right radicalism.
ROAD TO OSCARS
The best director award went to American filmmaker Brady Corbet for his 3-1/2 hour-long movie "The Brutalist", the epic tale of a Hungarian Holocaust survivor played by Adrien Brody, who seeks to rebuild his life in the United States.
The festival marks the start of the awards season and regularly throws up big favourites for the Oscars, with eight of the past 12 best director awards at the Oscars going to films that debuted at Venice.
The prize for best screenplay went to Murilo Hauser and Heitor Lorega for "I'm Still Here", a film about Brazil's military dictatorship, while the special jury award went to the abortion drama "April", by Georgian director Dea Kulumbegashvili.
Among the movies that left Venice's Lido island empty-handed were Todd Phillips's "Joker: Folie à Deux," starring Joaquin Phoenix and Lady Gaga, the sequel to his original "The Joker" which claimed the top prize here in 2019.
Luca Guadagnino's "Queer," with Daniel Craig playing a gay drug addict, and Pablo Larrain's Maria Callas biopic "Maria", starring Angelina Jolie as the celebrated Greek soprano, also won plaudits from the critics but did not get any awards.
The Venice jury this year was headed by French actress Isabelle Huppert.