As countries around the world grapple with an influx of people fleeing global crises, a jury led by Hollywood filmmakers Joel and Ethan Coen chose the gritty picture about Sri Lankan asylum-seekers by acclaimed French director Jacques Audiard among 19 international contenders.
"To receive a prize from the Coen brothers is something pretty exceptional," Audiard said, clutching the trophy.
"I'm very touched," he said.
The harrowing Holocaust drama "Son of Saul" by Hungarian newcomer Laszlo Nemes, offering unflinching depictions of the gas chambers of Auschwitz, claimed the Grand Prize, runner-up for best picture.
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And "The Lobster", a surreal, pitch-black comedy about modern love by Greece's Yorgos Lanthimos and starring Colin Farrell and Rachel Weisz, bagged the third-place Jury Prize.
Best director honours went to Taiwan's Hou Hsiao-Hsien for the visually lush, slow-burn martial arts film "The Assassin".
The nine-member panel handed the best-actress trophy to two winners: US star Rooney Mara for the lesbian love story "Carol" which also stars Cate Blanchett; and France's Emmanuelle Bercot, in the doomed romance "Mon roi" (My King) by fellow actress-turned-filmmaker Maiwenn.
"I am thrilled to share this with another actress because it's a bit too big for me to carry alone," said Bercot, who had opened the 12-day festival with French social drama "Standing Tall", which she directed and co-wrote.
Mexican director Michel Franco clinched best screenplay for "Chronic" starring British actor Tim Roth as a nurse caring for dying patients.
Audiard, a Cannes favourite, specialises in films about broken people looking for fresh starts, as in critical triumphs such as "A Prophet", "Rust and Bone" and "The Beat That My Heart Skipped".