The 18-year-old former junior world champion fell to the floor and kissed the mat after beating Nikita Glasnovic of Sweden 5-1 in a one-sided contest at the Carioca Arena 3 to secure a breakthrough bronze.
"I am so happy for Iranian girls because it is the first medal and I hope at the next Olympics we will get a gold," said Zenoorin.
"I am very excited and I want to thank my parents and my coach. They really stand behind me and I am so happy."
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Iran have won 65 medals at the Olympics in just four sports - wrestling, weightlifting, taekwondo and athletics - with Zenoorin's bronze the Asian nation's fifth medal in Rio.
(Writing by Patrick Johnston in Singapore; editing by Amlan Chakraborty)
