It tells the story of Rick Dalton (DiCaprio), star of westerns of the television, its double in the scenes of action (Pitt) and the neighbor of his, the actress Sharon Tate (Robbie). Al Pacino, Dakota Fanning, Bruce Lee and Steve McQueen are also part of the cast.
At the end of the projection, the audience stood and applauded Tarantino for seven minutes, 25 years after the Palme d'Or for "Pulp Fiction."
Pitt was visibly moved, while the British actress Tilda Swinton, who does not act in the film, could barely contain her tears.
"We'll see you at La Croisette!" Tarantino told the audience after thanking the spectators for their support.
Part of the international critics made their first reviews and considered it to be one of Tarantino's best films in years.
A critic of the British newspaper The Guardian called it "a brilliant comedy of black humor."
Deadline's web site assessed that Tarantino "was born to make this movie", "glorious" and "hilarious".
Cannes "changed the life" of the American director, 56 years.
"I came first with 'Dirty Dogs', as a small independent filmmaker, and then went around the world," he recalled.
Also on the red carpet, Pitt broke into praise for Tarantino, with whom he had worked for ten years in "Sacanas Sem Lei".
"It's a pleasure to work with him, he can not be compared to anybody […] He knows the film in an exhaustive way "and the film for him is" a love letter to Hollywood, Los Angeles. "
In the film, "we interpret two actors who try to find their place in a changing world," said DiCaprio, whose girlfriend, Argentine actress Camila Morrone, also watched the projection, though always separate.
Tarantino asked the audience yesterday not to reveal the contents of the film with an open letter that began with "I love the cinema, you love cinema, it's the journey of discovering a story for the first time."
"I'm thrilled to be here in Cannes to share "Once Upon a Time … in Hollywood" with the festival crowd. The cast and crew worked hard to create something original, and I just ask that everyone avoid revealing anything that would prevent the following audience from experiencing the movie the same way. "Thank you."
Following the message on social networks came the hashtag #NoSpoilersInHollywood [nada de spoilers em Hollywood].
Tarantino's story in Cannes is full of memorable scenes, beginning with the Palme d'Or delivered by Clint Eastwood 25 years ago to "Pulp Fiction."
When he received the prize, between applause and whistles, the American filmmaker raised his middle finger at a woman who shouted, "What the fuck! No, what the fuck!"
Ten years later, the filmmaker returned to La Croisette to perform "Kill Bill vol.2" outside the competition.
With "Sacanas Sem Lei", it returned to dispute the Palme d'Or in 2009, but this time the prize was with the Austrian Michael Haneke by "The White Ribbon".
However, he made his own on the red carpet while dancing with the French actress Mélanie Laurent. In 2014, also risked a few steps with Uma Thurman for the 20 years of "Pulp Fiction".
On Saturday, the filmmaker may join the select group of filmmakers with two Golden Palms, including Bille August, Francis Ford Coppola, Luc and Jean-Pierre Dardenne, Michael Haneke, Shohei Imamura, Emir Kusturica and Ken Loach.
Pedro Almodóvar and Terrence Malick, among other filmmakers, also vie for the festival's top prize.