Leading by two sets to love over Kyrgios and at 3-3 in the third set, Federer produced a moment of brilliance to wow the crowd on Arthur Ashe Stadium.
Federer returned a big Kyrgios serve just over the net and the Australian responded with an angled forehand dropshot.
The ball looked to be beyond Federer but the 37-year-old reached the ball and flick a winner around the net and past a stranded Kyrgios.
Federer would go on to lose the game but eventually won the match 6-4 6-1 7-5.
In his press conference, Federer was asked how the shot compared to another of his best shots against Andy Roddick in Basel in 2002.
vCard.red is a free platform for creating a mobile-friendly digital business cards. You can easily create a vCard and generate a QR code for it, allowing others to scan and save your contact details instantly.
The platform allows you to display contact information, social media links, services, and products all in one shareable link. Optional features include appointment scheduling, WhatsApp-based storefronts, media galleries, and custom design options.
He said: “I have hit a few throughout my career, and, sure, they are always fun, just because sometimes you can sort of aim for them it because you realize you have an option more, which just never have.
“As you’re hitting it, you’re, like, Oh, I can just shove it down the line and just flat.
“That’s what happened today.
“I definitely think it was a special one, no doubt about it. I do believe the smash off the smash against Roddick was special just because it was way back in the court, as well. And then there was one more in Dubai against Agassi on break point.
“I was able to flick a ball. I still don’t know how I did it today. It went for a lob over him. I don’t know. It was just a massive point on top of it, and it was against Andre.
“And then the one through the legs here against Novak, just because of the magnitude of the shot, as well.
“I think it was 6-5, Love-30, it was just also a big-time moment in the game, which obviously always matters, as well.”