The result means Medvedev will cede his position at the top of the world rankings come the end of the tournament, while Kyrgios will appear in his first US Open quarterfinal when he faces another Russian playing under a neutral flag, Karen Khachanov, on Tuesday.
Medvedev later said he had struggled physically on the court, but added that Kyrgios outplayed him in the last two sets.
“Today, I felt a little bit sick,” he told reporters after the match. “The thing is in the USA I get sick one time for sure in the swing because the AC (air conditioning) is just crazy. Last year it happened in Cincinnati.”
“I felt my throat a little bit today … At the same time, it’s not an excuse at all because Nick played good.”
It was the fourth time Kyrgios had beaten Medvedev in five meetings and the second time in as many months after victory in Montreal.
The Australian saved several set points in a close first-set tie break — the first set Medvedev had dropped in the tournament — before falling behind in the second set when he dropped serve twice.
Medvedev leveled the match, but momentum swung in Kyrgios’ favor when he won five straight points on Medvedev’s serve in the fourth game of the third set.
The 23rd seed always looked the favorite to win the match from there, breaking twice in the fourth set to seal the victory in close to three hours. He ended the encounter with 53 winners, 21 of which were aces.
“I just thought I played the right way,” Kyrgios told reporters. “I returned unbelievable today. Just thought the third and fourth set were just so free. I was just having a lot of fun, embracing every moment out on Ashe (Arthur Ashe Stadium) today. Really proud of that.”
“I feel like I’m more just proud of the way that I’ve bounced back after everything, honestly,” he said. “I’ve been in some really tough situations mentally, and in some really scary places.
“Obviously if you look at it on paper, I probably wasn’t expected to win that. Maybe take a set or two if I’m lucky … I just sit there in the locker room after and I’m just super proud of the performance because there was really a time where I didn’t think I was capable of producing and doing this anymore.”