The 17th-seeded Kyrgios won the last five points after falling behind 5-2 in the tiebreaker.
The focal point of Kyrgios's new-found maturity was in the third set.
It was a match that was full of unusual distractions but Nick Kyrgios did not let them get to him. I didn't really know what was going on.
Yeah, today I think we can resume this match like this'. He beat me in a three-set battle. I mean, it's an opportunity to get a message across.
Kyrgios has been untouchable with his serve in 2018 and is putting a ton of pressure on his opponent to play a ideal match.
Asked about the prospect of facing Kyrgios, and the majority of the crowd, Dimitrov said: "I've done it many times before". He's a champion of the game. "I got it for free".
"I felt like the atmosphere completely changed", Kyrgios said.
"It was incredible", he said. No joke, he's like my favourite actor. "I just wanted him to think I was cool!"
"It was surreal seeing him tonight ..."
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The third set was an exhibition of serving from both men. I was kind of staring at him.
In response to the chair umpire attempting to take control, Tsonga then added: "He [a member of the crowd] said something to me and I do what I want". "I played a pretty good level in the tiebreak". He was really genuine.
Fast forward 12 months and the Kyrgios we saw defeat Viktor Troicki in straight sets had us rubbing our eyes to make sure we weren't hallucinating.
For an Australian public desperate to see a first home-grown victor of the men's national title since 1976, a seemingly reinvigorated Kyrgios could be the redemption story of the tournament. The victor of their last 16 encounter here will face either Kyle Edmund or Andreas Seppi in the quarter-finals.
Svitolina will now face 15-year-old sensation Marta Kostyuk who became the youngest woman to reach the third round since Martina Hingis got to the quarter-finals in 1996.
Whether you love Kyrgios or hate him - and if you read the comments section at the end of any Australian newspaper story that mentions him, you know he has quite a few haters - you can't knock his conduct during the first week of the Australian Open. I just had to find a way again, simple as that. What are the other options? I didn't play good tennis on the big point.
Kyrgios broke in the third game of the third set but what looked like being a routine victory when he served at 5-4 hit a snag as, out of nowhere, he dropped serve.
The Australian failed to go beyond the second round of a major in 2017 but appears fully focused and up for the task at the first Grand Slam of this season as he booked a fourth-round tie with Grigor Dimitrov.
Nadal said: "I needed hours on court, hours of practice, hours of playing sets with different players". A rogue "fan" interrupted the second set when he stood up and started yelling right behind the 22-year-old as he was about to serve, a helicopter parked itself above Hisense Arena and made it impossible for players to hear and technical difficulties caused a ruckus. "I've always played the same way".