Kelmendi edged out Japan's Misato Nakamura in the semi-final on a single penalty, then beat Odette Giuffrida of Italy to secure a stunning and historic gold medal.
Rio marks the first Olympics at which athletes are competing under the flag of Kosovo, which proclaimed independence from Serbia in 2008.
Kosovo was accepted as a member of the IOC in 2014 and now it has an Olympic champion in Kelmendi.
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The twice world champion, who was Kosovo's flag bearer at Friday's opening ceremony, represented Albania at the London Games in 2012 but did not win a medal on that occasion.
"I have lived four years for this day, for this moment, and I felt so happy there at the podium when I saw my flag and when I heard my anthem," she said.
There is no money in the world, no millions in the world which can make me feel how I feel today.
Kosovo's Majlinda Kelmendi (white) celebrates after defeating Japan's Misato Nakamura
Image credit: AFP
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