The Spaniard dropped a set for the first time during the tournament and was pushed hard by the plucky Argentine, but ultimately composed himself to reach the last-eight.
In the second set, which consisted of three breaks of serve apiece, had to be decided by a tiebreaker after the scores were tied at 6-6.
Spain's Rafael Nadal on Sunday defeated Argentina's Diego Schwartzman 6-3, 6-7 (4-7), 6-3, 6-3, clinching a place in the Australian Open quarterfinals. Once he moved 4-3 in front, Nadal stepped it up and broke the Argentinian. "I was like, "I got to break the ice, I got to say something".
Kyrgios appears to have largely won over a sceptical Australian public with his professional attitude this tournament, focusing throughout matches and showing that he does care about tennis after all.
"[I know] people think I'm cool, but I just wanted him to think I was the coolest person ever".
"It was a close first set and I didn't feel I got the best start", he said. "We had a lot of tough rallies so I was really glad how I stayed in there mentally".
Having lost the first set 6-3, he recovered from a break down three times to take the second set on a tiebreak - the first set Nadal had lost. You know, like you said, just that constant, just, working at everything, my game, on and off the court. If his match against Novak Djokovic at last year's French Open is any indication of his talent, Nadal will be up against a feisty opponent.
Russian Federation at United Nations warns collapse of Iran deal would be 'alarming'
Despite this, fears have heightened this week as Kim Jong-un appears to be not willing to surrender his nuclear weapons. United States President Donald Trump accuses Russian Federation of aiding North Korea to avoid worldwide sanctions.
"[There] have been very, very tough conditions yesterday and today", Nadal said.
He's a great player in all aspects.
The win took the 31-year-old's Australian Open record to 54-11 as he chases his second Melbourne title after beating Federer in the 2009 final.
He went into this clash on a seven-match winning streak, which included victory over Dimitrov in the semi-finals of the Brisbane International earlier this month.
"I was very nervous ..."
After a tight tussle in the opening four games against No. 19-seeded Rybarikova, a Wimbledon semifinalist past year, Wozniacki dominated the fourth-round match and conceded only six points in the second set. I was a little bit up and down on some service games, and he was returning quite good.
On his third match point, Nadal hit a back-hand victor to seal the victory, advancing to the quarterfinals for the 10th time. No. 17 Madison Keys beat Ana Bogdan 6-3, 6-4; Naomi Osaka beat No. 18 Ashleigh Barty 6-4, 6-2; No. 20 Barbora Strycova beat Bernarda Pera 6-2, 6-2; No. 21 Angelique Kerber beat Maria Sharapova 6-1, 6-3; Hsieh Su-wei beat No. 26 Agniezska Radwanska 6-2, 7-5.