The Russian advanced after serving 12 aces and converting six of his twelve break chances, outlasting his 22-year-old opponent.
Wu became the first Chinese participant in the third round of the US Open.
But he found it challenging to handle Medvedev’s constant pressure.
Since Roger Federer’s five straight US Open victories between 2004 and 2008, Medvedev has been attempting to become the first player to do it.
But if Kyrgios, the Wimbledon runner-up, wins the following round, Medvedev will drop out of the top spot.
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After the competition, Rafa Nadal, the champion of the Australian Open and the French Open, and emerging sensation Carlos Alcaraz may tie for first place in the men’s rankings.
Kyrgios defeated JJ Wolf, continuing his upward trajectory. Australian defeated his American opponent 6-4, 6-2, 6-3.
Casper Ruud, the fifth seed, defeated Tommy Paul in five sets to get to the US Open fourth round.
Ruud of Norway, who earlier this year fell to Rafael Nadal in the French Open final, defeated the American in four hours and 23 minutes, winning 7-6 (7-3) 6-7 (5-7) 7-6 (7-2) 5-7 6-0.
After the competition, four players, including Ruud, will be vying for the title of world number one.
Corentin Moutet, a lucky French loser, will be his next role. Moutet overcame Pedro Cachin of Argentina. 6-3 4-6 6-2 7-5.
In New York, 13th seed Matteo Berrettini ruined Andy Murray’s season by defeating Australian Alex de Minaur 6-1, 6-1, 3-6, 7-6 (7-5). Pablo Carreno Busta of Spain defeated Alex de Minaur.
