Cooper, who had already made history as the youngest person ever nominated for supporting actor in a limited series, told the audience at the 77th Emmy Awards that he was "nothing" just three years ago.
"Honestly, when I started these drama classes a couple years back, I didn't expect to be even in the United States, never mind here," the 15-year-old English actor said in his acceptance speech.
"But I think tonight proves that if you listen and you focus and you step out of your comfort zone, you can achieve anything in life."
Hollywood stars arrived at the Peacock Theatre in Los Angeles on Sunday night for the ceremony, hosted by US comedian Nate Bargatze.
"It says my name on the statue, but it really belongs to all of the people who worked on the show," Cooper said.
Co-star Erin Doherty won best supporting actress in a limited series, dedicating the award to her older sister.
Severance was nominated 27 times, while crime drama mini-series The Penguin had 24 nominations and Adolescence received 13.
The British drama, which dominated Netflix's most-watched list earlier in 2025, centres on the story of a 13-year-old boy arrested for the murder of a classmate.
Adolescence director Philip Barantini took home the Emmy for outstanding directing for a limited or anthology series or movie, while writers Jack Thorne and Stephen Graham won for outstanding writing in the same category.
"To Netflix, thank you for trusting us with this mad idea," Barantini said while accepting his award.
The night's other major winners included Seth Rogen's The Studio, which took home awards for best directing, best writing and outstanding actor in a comedy series.
Before the ceremony, fellow nominee Jake Gyllenhaal surprised Cooper during an interview ahead of the 77th Emmy Awards, leaving the young Adolescence star momentarily speechless.
Asked moments earlier how he would react if they met, Cooper said: "I don't know. I'll just stare at him. I don't really know."
The pair hugged, and Gyllenhaal gave Cooper a small gift - a "lucky duck".
"I made this movie (Brokeback Mountain), and I got nominated for an Academy Award, and a friend of mine sent me this before. Something just like this," he said.
"It's just a 'Lucky Duck' to keep in your pocket. To give you a little bit of luck."
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