As countries around the world grapple with an influx of people fleeing crises, a jury led by American filmmakers Joel and Ethan Coen chose the gritty picture about Sri Lankan asylum-seekers by acclaimed French director Jacques Audiard from a field of 19 international contenders.
"To receive a prize from the Coen brothers is something pretty exceptional," Audiard said after a victory that surprised many critics at cinema's top showcase.
The harrowing Holocaust drama "Son of Saul" by Hungarian newcomer Laszlo Nemes, offering unflinching depictions of the gas chambers of Auschwitz, claimed the runner-up Grand Prize.
"Europe is still haunted by the destruction of the European Jews," Nemes said.
"I wanted to approach this history in a different way" to reach a younger generation, he said.
Surprise best actress win
"The Lobster", a surreal black comedy about modern love by Greece's Yorgos Lanthimos and starring Colin Farrell and Rachel Weisz, bagged the third-place Jury Prize.
The best director honour went to Taiwan's Hou Hsiao-Hsien for the lush, slow-burn martial arts film "The Assassin".
In one of the night's biggest upsets, the nine-member panel handed the best-actress trophy to two winners.
Rooney Mara, paired in the American lesbian love story "Carol" with more hotly tipped co-star Cate Blanchett, split the prize with France's Emmanuelle Bercot, in the doomed romance "Mon Roi" (My King).
Mara did not attend the ceremony, leaving her director Todd Haynes to pick up her trophy.
Bercot also opened the Cannes fest with a film she directed, "Standing Tall".
In a big night for the host country, France's Vincent Lindon won best actor for his moving turn as a job-seeker trying to preserve his dignity in "The Measure of a Man".
French Prime Minister Manuel Valls hailed the homegrown winners in a tweet: "French cinema shines tonight in Cannes and out into the world".
President Francois Hollande's office praised "Dheepan" for "dealing with virtuosity with the painful subject of Tamils looking to build a future in Europe".
Mexican director Michel Franco clinched best screenplay for "Chronic" starring British actor Tim Roth as a nurse caring for dying patients.
'Strangers in foreign land'
However, critic Peter Bradshaw of London's The Guardian expressed disappointment at the choice of "Dheepan", saying it was more of a lifetime achievement award for Audiard, a Cannes favourite.
The "brilliant director... had actually given us something less than his very best work," Bradshaw said of Audiard, whose movies include "A Prophet" and "Rust and Bone".
Joel Coen indicated that the jury had been divided.
"To some degree or another we all thought it was a very beautiful movie," he told reporters.
"We're different people, some people had greater enthusiasms for other things or lesser, but in terms of this movie, everybody had... some high level of excitement and enthusiasm for it.
In "Dheepan", novelist and former child soldier Anthonythasan Jesuthasan plays an ex-Tamil Tiger fighter escaping Sri Lanka's brutal civil war.
He and two strangers -- a woman and a nine-year-old girl -- pretend to be a family to get to France on fake passports.
Once they arrive in a rough housing estate on the outskirts of Paris, the makeshift family bonds and Dheepan must use his battlefield experience to keep the three of them safe from drug gangs.
Anthonythasan himself fought for the Tamil Tigers from the age of 16 before making it in 1993 on a fake papers to France, where he was granted political asylum.
Audiard told reporters during the festival that he "couldn't have placed Sri Lanka on a map" when he began the project.
On Sunday, he said he started working on the picture long before the current refugee crisis in Europe in which more than 1,700 people are estimated to have drowned in the Mediterranean this year.
"What interested me was the position of someone different in society. These people who sell roses to us when were sitting in a cafe, where they come from," he said.
"If it helps the situation, then so much the better."
Actor Jake Gyllenhaal later said he was one of the film's biggest champions on the jury.
"Over the course of two hours we watch three strangers forced to travel to a foreign land essentially learn to love each other, which is something I've never really seen done in the way it is in that film," he said.