Yet Kyrgios' level dipped alarmingly after he was broken in game 10 and a Federer triumph appeared inevitable thereafter.
And what an opportunity it is: the great Federer on tennis's biggest stage after the Swiss denied Nick Kyrgios an all-Australian showdown with Millman with a 6-4 6-1 7-5 dispatch of the Canberran in a vintage display.
And, just like any Federer match, he hit an absolutely ridiculous shot, arguably the best of the tournament so far.
With Kyrgios one point away from going up 4-3 in the third, Federer pulled out a magical shot around the post that earned him an ovation from the crowd in NY. Nick fought back to hold serve, but Federer went on to close out the match in straight sets, 6-4, 6-1, 7-5.
"At 3-All, Love-40, I take one of those points, the match is wide open", Kyrgios said.
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"I think if he breaks there he probably runs away and wins that first set", Federer said.
"For a shot like this to happen in a practice, you will will be running into a fence and you will hit it into the net".
Up two sets to love, the 37-year-old Swiss superstar defied his years to reach an acutely-angled Kyrgios slice, flashing a victor around the post of the net to take the game back to deuce.
Vondrousova, through to a Grand Slam third round for the first time, will play Ukraine's Lesia Tsurenko, who defeated Czech Katerina Siniakova 6-4, 6-0 after taking out Wozniacki in the second round.
When Federer lost to Djokovic in the Cincinnati Masters final, a lot of people said his legs looked exhausted.
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Federer later explained that it was one of the more "unique" shots in his career.
Federer was asked about the shot following his win over Kyrgios and he explained why it felt so "special". A little compulsive - John Millman, who will face Federer for a place in the quarter-finals, admitted he was a handful for his parents when he was growing up in Brisbane. On the men's side, I can not even think about returning John Isner (6ft 10in/2.08m) or Kevin Anderson (6ft 8ins/2.03m) or somebody like this.
Meanwhile, Joao Sousa won three tiebreakers in his 7-6 (7-5) 4-6 7-6 (7-4) 7-6 (7-5) victory over 17th-seeded Frenchman Lucas Pouille.
Wimbledon champion Novak Djokovic headlined the evening action on Ashe against French veteran Richard Gasquet.
The 37-year-old Swiss battled through a tough opening period of the match before exerting his dominance over the 23-year-old Australian, winning 6-4 6-1 7-5 to book his spot in the last-16.
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A break at that point could have put serious doubt in his opponent's mind, but Federer weathered the storm, and after seven deuces and four break points saved, holding serve felt like a victory.