As it turned out, however, Kyrgios was no match for Federer on the day, as the Swiss ace wrapped up a 6-4, 6-1, 7-5 victory in just one hour and 46 minutes to book his place in the fourth round.
Federer did have one piece of advice for Kyrgios - sometimes it's the conservative approach that pays off and not the flashy crowd-pleasers.
Federer returned Kyrgios' thunderous serve who then pulled off a nice little shot himself, with the Swiss legend sprinting towards the ball.
APNick Kyrgios left gobsmacked by Roger Federer.
"I think if he breaks there he probably runs away and wins that first set", Federer said. If I want it enough, you know, I have a coaching option, psychology option.
"Some of his behaviour that is questioned". But, I mean, obviously I want to achieve more in the sport.
Midway through the third set with the game tied at 3-3, Kyrgios thought he caught the 37-year-old out with a deft drop shot.
It prompted a trademark Kyrgios dummy spit where he was seen swearing in the direction of his players box.
"I take one of those points, the match is wide open", Kyrgios said. The crowd was up on its feet to acknowledge what is yet another addition to "Federer hot shots".
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Next is what shapes up as a mismatch, facing 55th-ranked John Millman, who never before has made it this far at any Grand Slam tournament.
Federer will face unseeded world No. 55 John Millman in the fourth round who recorded consecutive four-set wins over No. 14 seed Fabio Fognini and unseeded Mikhail Kukushkin.
This will be Thiem's first quarterfinal at a major other than the French Open and his first match against Nadal on a surface other than red clay.
Speaking after the game, Federer enjoyed his handy work saying it was one of the greatest shots in his illustrious career.
The daring ploy didn't pay immediate dividends, but it wasn't long before Federer was looking unsettled as Kyrgios continued to apply niggly and offbeat tactics. There was cheek, too, as he performed an imitation of the Federer service action while leading 40-0 in the fourth game.
It denied Kyrgios a game point, although the Aussie would hold to lead the third set 4-3.
Federer, of course, is in search of his 20th Grand Slam singles title.
Federer hasn't won the US Open since 2008.