The film set in the early 1980s centres around a queer family in Chile and the onset of the AIDS epidemic.
"This award doesn't celebrate perfection. It celebrates that fear, that stubbornness to exist just as we are, even when it makes others uncomfortable," said Cespedes while accepting the prize.
This year's Un Certain Regard section, which usually focuses on more art-house fare, was particularly strong, with several promising directorial debuts from actors including Scarlett Johansson, Harris Dickinson and Kristen Stewart.
Once Upon a Time in Gaza, which follows a low-level drug dealer and his underling in the coastal enclave the year the Islamist group Hamas took over, earned a directing award for Palestinian twin filmmakers Arab and Tarzan Nasser.
To everyone in Gaza, "to every single Palestinian: your lives matter and your voice matters, and soon Palestine will be free," said Tarzan Nasser, eliciting a standing ovation.
Colombian director Simon Mesa Soto's dark comedy exploring the art world, A Poet, received the runner-up Jury Prize.
Frank Dillane, who stars in Dickinson's well-received debut about a homeless man, Urchin, took home best performance along with Cleo Diara, who stars in Portuguese director Pedro Pinho's exploration of neo-colonialism, I Only Rest in the Storm.
The screenplay award went to British director Harry Lighton and his Alexander Skarsgard-led kinky romance Pillion.
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