The drama by Ildiko Enyedi, one of four female filmmakers in competition, features graphic scenes in an abattoir set against the budding romance of two people who share a recurring dream.
The win marked an upset at the 11-day Berlinale, where a European refugee comedy by cult Finnish filmmaker Aki Kaurismaki, "The Other Side of Hope", had been the odds-on favourite.
Kaurismaki took the Silver Bear for best director.
Enyedi thanked the festival for embracing her first full-length feature in 18 years but said working conditions in Hungary were growing more difficult under Prime Minister Viktor Orban.
"We live in a more and more absurd country, frighteningly absurd country," she told reporters after the ceremony, while adding that the state film fund served as a "sort of island".
"We can work there at relative freedom, peace and we get professional support."
The runner-up jury prize went to Franco-Senegalese filmmaker Alain Gomis for "Felicite" about a Kinshasa nightclub singer who has to scrape together funds to pay for her son's treatment after a serious road accident.
South Korea's Kim Min-Hee, the star of Hong Sang-Soo's intimate drama "On the Beach at Night Alone" about a failed love affair with a director, won best actress.
And Austria's Georg Friedrich scooped best actor for his role in the German drama "Bright Nights" as a mourning father who takes his teenage son on a road trip through Norway.
'Fight the dark ages'
Best screenplay went to another favourite of the festival, "A Fantastic Woman" by Chile's Sebastian Lelio, starring transgender actress Daniela Vega.
Lelio, joined on stage by Vega, said the film about a singer fighting for her right to attend the funeral of her much older lover was a call for tolerance in trying times.
"We have to fight the dark ages with beauty, with elegance, with poetry," he said.
Best documentary, awarded for the first time at the festival, was picked up by Palestinian director Raed Andoni for "Ghost Hunting".
The film recreates a notorious Israeli interrogation centre - and has ex-prisoners re-enact experiences in a bid to free them of their demons.
"We still have 7,000 Palestinians living in those jails... They never get the recognition as I do," said Andoni, who also served time behind bars in Israel.
Capping a politically charged year at the festival, US documentary jury member Laura Poitras ("Citizenfour") said filmmakers must stand up for basic freedoms.
"Yesterday the president of the United States described the press as the enemy of the people," she said, referring to a tweet by Donald Trump on Friday.
"As documentary filmmakers we're here to say that we're the enemy of nationalism and of exclusion."
Jury 'fell in love'
A seven-member jury led by Paul Verhoeven ("Basic Instinct", "Elle") and including US actress Maggie Gyllenhaal ("The Dark Knight") and Mexican director and actor Diego Luna ("Rogue One: A Star Wars Story") selected the main prizes among 18 contenders.
Last year, jury president Meryl Streep gave top honours to Italy's "Fire at Sea", a portrait of the refugee crisis on the island of Lampedusa. It is nominated for an Academy Award for best documentary this month.
Presenting the Golden Bear, Verhoeven said the jury "fell in love" with "On Body and Soul", adding that it was about "two people connecting in quite an amazing way".
The enigmatic film features Endre and Maria, who by day work in a slaughterhouse but by night have the same dream about a male and a female deer nuzzling in a snowy forest.
Endre, the abattoir's financial director, has a deformed hand that makes him self-conscious while Maria, the new quality control inspector, is crippled by shyness and an obsessive-compulsive disorder.
Enyedi contrasts the growth of their relationship and the petty squabbles at the company with stomach-churning scenes of the cattle bound for the butcher's hooks.
Film industry bible Variety said the film "blends mournfully poetic whimsy with stabs of visceral brute reality".