Mendes was favourite to win in the category for his First World War drama 1917, but it was Bong who reigned supreme.
Spike Lee announced the news, which caused the audience to stand on their feet to applaud the filmmaker.
Bong becomes the first South Korean filmmaker to win the award.
"After winning Best International Feature, I thought I was done fo the day and ready to relax," he quipped.
For the remainder of his acceptance speech, Bong paid tribute to his fellow directors, including Martin Scorsese and Quentin Tarantino.
"When I was in school, I studied Martin Scorsese's films – just to be nominated was an honour; I never thought I would win."
The black comedy was the evening's biggest winner, making history by becoming the first ever foreign language film to win Best Picture.
Other winners at the 2020 ceremony included Brad Pitt, who delivered an emotional acceptance speech that saw him praise Leonardo DiCaprio and criticise the verdict of Trump's impeachment trial, while Laura Dern took home the prize for Best Supporting Actress.
Meanwhile, Olivia Colman had the audience in stitches before presenting Phoenix with his award.
Find a full list of the 2020 Oscar winners here.
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