Kyrgios, seeded No. 23, beat Medvedev in four sets 7-6, 3-6, 6-3, 6-2 in New York.

Australian tennis legend Todd Woodbridge described the match as the best of Kyrgios' career and he has moved into a perfect position to win his first grand slam.

Medvedev was the defending champion, but Kyrgios made light work of the Russian to set up a quarter-final showdown with Karen Khachanov.

"It might have taken him 27 years, but he's playing the best tennis of his life," Woodbridge said. "He's a real contender to win his first [singles] grand slam title. That's his greatest match in a grand-slam tournament."

Kyrgios made of a mockery of the rankings and has blown the US Open wide open with a rollicking fourth-round win over Medvedev.

In an explosive encounter laced with controversy and drama, Kyrgios risked being defaulted and overcame a running verbal battle with the chair umpire before ousting the top seed.

It was the Wimbledon runner-up's second defeat of Medvedev in three weeks and vaulted Kyrgios into the quarter-finals at Flushing Meadows for the first time.

At last realising his rich potential, the 27-year-old will play another Russian, Khachanov, for a semi-final berth on Tuesday (Wednesday AEST).

"There was a lot of pressure on [Medvedev's] shoulders, but I played really well," Kyrgios said.

"I've been playing amazing the last couple of months, but what a place to do it. A packed out in New York, I'm extremely blessed.

"I'm just trying to work hard every day, make every practice session count and getting to sleep, I probably would be out every night before. I'm just really happy, hopefully I can keep it going.

"I don't want to let [my team] down. We've been on the road now for four months ... I want to make it count. I want to go all the way, hopefully it's possible."

Kyrgios's former long-time girlfriend Ajla Tomljanovic was also playing her fourth-round match on Sunday against in-form Russian Liudmila Samsonova, striving to give Australia two quarter-finalists in New York for the first time this century.

Now three wins away from breaking his grand slam title duck, Kyrgios was imperious at times.

He received a standing ovation from the Arthur Ashe Stadium crowd after winning a pulsating opening set that stretched more than hour.

Other times, he flirted with disaster.

He looked to have thrown away the first set after giving up a 4-2 lead and then a 4-1 advantage in the tiebreaker, not to mention threatening to hit the self-destruct button and engaging in an unnecessary, elongated exchange with Greek umpire Eva Asderaki-Moore.

The combustible Canberran lambasted Asderaki-Moore for starting the shot clock apparently too early.

"You are the only umpire that I've a problem in this matter," Kyrgios fired at her.

"Use your common sense. Just use it a little bit."

But, after regaining his cool and fighting off three set points, Kyrgios brought up a fourth of his own with an exquisite backhand drop shot that almost spun back over onto his side of the net.

It was probably the shot of the entire match and he duly nabbed the set when Medvedev sent a forehand wide after 63 minutes of quality tennis.

But it wasn't long before tensions really boiled over.

Medvedev fumed at the umpire for not warning Kyrgios after the Australian, frustrated at going down an early break in the second set, went within centimetres of hitting a ball into the first row of the stands, and likely a spectator.

Medvedev then threatened to quit if someone from Kyrgios's courtside entourage wasn't ejected for disrupting the top seed between his first and second serves.

"They cannot do it," Medvedev raged.

"If they do it a second time, I am not playing they're out, until somebody is out."

After levelling the match at a set apiece, Medvedev received an extraordinary, possibly unprecedented, gift from Kyrgios.

After looking to have earned a break point in the second game of the third set, when Medvedev couldn't return a ball, Kyrgios ran around the net celebrating and hit the ball away for a mock winner.

Quite rightly, though, Asderaki-Moore awarded the point to Medvedev because the Russian's shot, while clearly not going over the net, was "still in play".

"I thought it was legal," Kyrgios said, shaking off the blunder, somewhat uncharacteristically, before breaking Medvedev on his next service game to claim a 3-1 lead, then going on to seize a two-sets-to-one lead.

Kyrgios turned the screws with another break in the third game of the fourth set, then received an audible obscenity the following game.

But it didn't matter as Kyrgios snared a double break and powered to a 20th victory in his past 23 matches after two hours and 53 minutes.

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