Shavdatuashvili, the 20-year-old who only just qualified for the Games, landed an early Yuko score to take command and held off all Ungvari's attacks to close out victory.
Japan's Masashi Ebinuma took bronze after beating Poland's Pawel Zagrodnik with an Ippon.
Republic of Korea's Cho Jun-ho also claimed bronze on judges' decision over Spaniard Sugoi Uriarte at the end of golden score.
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