The first Asian woman to take home the same award was Yoko Shimada, who won in 1980 for her role in Shogun. Oh previously won a Golden Globe in 2006 for her supporting role on Grey's Anatomy.
Oh, who was also co-hosting the event with Andy Samberg, won the award for her role in Phoebe Waller-Bridge's BBC drama series Killing Eve, and thanked her parents in Korean during the acceptance speech.
"Mostly, there are two people here tonight that I am so grateful that they are here with me. I'd like to thank my mother, my father," she said.
Oh added “엄마! 아빠! 사랑해요” (which translates to “I love you, mom and dad” according to Vulture), and bowed to her parents as they did the same back.
The speech was soon shared on social media, with fans adoring the heartwarming moment.
Oh has also been praised for her stint as host of the awards alongside Samberg. The duo impressed with their joke-filled opening monologue during, in which they lovingly poked fun at several of this year's nominees.
The evening, designed to award the best in film and television, saw wins for Green Book, The Marvelous Mrs Maisel and Bohemian Rhapsody, which was the unexpected recipient of the ceremony's biggest award. You can find a full list of winners here.
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