"This is pretty crazy, I'm not really crying ...
"The incredible cast and crew of Euphoria, I'm so lucky to go to work with you every day and I'm inspired by everything you do.
"To Sam Levinson, I appreciate you so much, you're my family, I'm so grateful for Rue and I'm grateful you trust me with your story, I hope I continue to do you proud."
Zendaya then went on to praise the efforts of young people offering "hope" to the world.
She said: "I know this feels like a weird time to be celebrating, but there is hope in the young people - our TV show may not always feel like that - but there is hope in the young people and I want to say to all my peers doing the work in the streets, I see you, and admire you and I thank you."
On Euphoria, Zendaya plays Rue Bennett, a teenage drug addict struggling with recovery and sobriety on the series exploring trauma and identity among teenagers.
The 24-year-old is the youngest ever to win in the category, overcoming a strong group of nominees including Jennifer Aniston, Olivia Colman, Jodie Comer, Laura Linney and Sandra Oh.
She's not the first young actress to take out older competition at this year's awards. Julia Garner also beat Meryl Streep and Laura Dern to an Emmy for Outstanding Supporting Actress with her role in Ozark.
- Additional reporting, NZ Herald