Stefanos Tsitsipas takes down Roberto Bautista Agut 7-5, 4-6, 6-4, 7-6 to make it to the Australian Open semifinals after an intense back-and-forth tiebreak. (0:34)

Rafael Nadal won all of his service games and ended 21-year-old American Frances Tiafoe's best run at a major with a dominating 6-3, 6-4, 6-2 victory in the Australian Open quarterfinals.

Against Tiafoe, who previously had never been past the third round in a major, Nadal won 20 of the first 23 points in his service games and erased the only two break points he faced, both early in the second set.

Nadal has won every set he has played in the tournament so far, the first time he has done that en route to the semifinals in Australia since 2009, the only time he won the title.

Rafael Nadal has looked strong at the Australian Open, having won every set he has played so far at the tournament. Jason Heidrich/Icon Sportswire

"I feel lucky to be where I am after all the things I went through," said Nadal, who quit during his quarterfinal at Melbourne Park a year ago because of a right leg problem, quit again during his semifinal at the US Open in September because of a painful right knee, and then had offseason surgery on his right ankle.

"Not easy situations," he said, summing it up.

Nadal, 32, reached his 30th major semifinal and prevented Tiafoe from getting to his first, two days after he turned 21.

"I knew he was going to bring crazy intensity," Tiafoe said. "I knew the ball was going to be jumping. I knew if he got hold of a forehand, it was going to be barbecued chicken. But point in, point out, I've never seen someone so locked in."

Nadal reached his 30th Grand Slam semifinal and next faces Stefanos Tsitsipas, 20, who eliminated two-time defending champion Roger Federer in the fourth round and took care of No. 22-seeded Roberto Bautista Agut of Spain 7-5, 4-6, 6-4, 7-6 (2) on Tuesday.

A post-millennial through and through, Tsitsipas sounded as excited about doubling his YouTube channel's followers to more than 30,000 within a few hours -- "Oh my god, really?" -- as he was about becoming the youngest Grand Slam semifinalist since 2007.

"Guys," he urged people watching the Australian Open on Tuesday in person or on TV, "if you haven't subscribed, please subscribe."

Lest anyone get the idea that Tsitsipas' stunning victory over Federer at Melbourne Park was a fluke, he followed it up by becoming the first player from Greece to reach the final four at a major tournament.

"I knew that win against Federer was important, played a huge role in my image -- like, who I am," said Tsitsipas, who eliminated the Swiss in the fourth round Sunday. "But I knew that the biggest challenge was today's match, that I can prove myself once again."

Cheered on by a loud, flag-waving contingent of Greek fans inside and outside Rod Laver Arena, Tsitsipas displayed his varied toolbox, producing 22 aces, 30 more winners than unforced errors (68-38) and a nose for getting to the net.

It was a terrific encore to what he did against his idol, the 37-year-old Federer, in a result that left Tsitsipas unable to sleep.

Tsitsipas was down a break in the first and third sets before turning both around against Bautista Agut, whose own thrill ride to the quarterfinals included victories over three-time major champion Andy Murray and Marin Cilic, the 2014 US Open champion and the runner-up to Federer at Melbourne Park a year ago.

"Well, he's a good player, no? He's very complete. He has a good forehand and backhand. He's serving well," Bautista Agut said about Tsitsipas. "I think he knows the game. He knows how to play."

That's why his peers voted him the 2018 Most Improved Player. And why he's already in the top 20, seeded 14th in Australia.

Stefanos Tsitsipas, 20, is the youngest man to reach a Grand Slam semifinal since 2007. Lynn Bo Bo/EPA

Tsitsipas recently was asked what his goal was for this season. The reply: reaching the semifinals at a major. Well, we're all of three weeks into 2019 and that box is checked.

So is he satisfied?

"That's like the starting point to go deeper," Tsitsipas replied. "That's like the minimum, I would call it."

No man as young as Tsitsipas had advanced this far at any Grand Slam tournament since Novak Djokovic at the 2007 US Open or at the Australian Open since Andy Roddick in 2003.

"It all feels like a fairy tale, almost. I'm just living the dream, living what I've been working hard for," said Tsitsipas, who dropped his racket, fell on his back and covered his face with his hands at match's end. "I mean, I feel a bit emotional but not too much because I know I worked hard to get here."

The Associated Press contributed to this report.