The result means Medvedev will relinquish his top spot at the end of the tournament, while Kyrgios will appear in his first US Open quarter-final when he faces another Russian playing under a neutral flag, Karen Khachanov, on Tuesday.
Medvedev later said that he struggled physically on the court, but added that Kyrgios outperformed him in the last two sets.
“Today I felt a bit sick,” he told reporters after the match. “The thing in the States is that I’m definitely going to get sick once in the hammock because the air conditioner is crazy. This happened last year in Cincinnati.”
“I got a little pissed off today…At the same time, that’s no excuse at all because Nick played so well.”
It was the fourth time Kyrgios had defeated Medvedev in five meetings and the second time in as many months after his victory in Montreal.
The Australian saved several points in the first game from breaking the tie – Medvedev’s first set in the tournament – before falling behind in the second when he was served twice.
Medvedev leveled the match, but momentum swung in Kyrgios’ favor when he won five consecutive points on Medvedev’s serve in the fourth game of the third set.
The 23rd seed always looked like the favorite to win the match from there, breaking twice in the fourth set to take the win in nearly three hours. He finished the showdown with 53 winners, 21 of whom were aces.
“I just thought I played the right way,” Kyrgios told reporters. “I was incredibly back today. Just thought the third and fourth sets were so free. I was having so much fun, embracing every moment at Ashe (Arthur Ashe Stadium) today. Really proud of that.”
“I feel more proud of the way she wore it after all, honestly,” he said. “I’ve been through some really tough situations mentally, and in some really scary places.
“Obviously if you look at it on paper I probably wouldn’t have expected to win that. I might take a set or two if I’m lucky… I sat there in the locker room afterwards and I’m very proud of the performance because there was really a time when I didn’t I didn’t think in him that I could produce and do this anymore.”
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