"How much (do) you have to pay Svitolina to have a one-hour lesson - I got it for free", Kostyuk joked. "After a while without being on the competition. second victory in a row, that's very important".
Ninth seed Stan Wawrinka had a tough time of things against world number 136 Ricardas Berankis, eventually prevailing 6-3 6-4 2-6 7-6 (2).
Kyrgios won the final set 7-6 to advance out of the Round of 64 match.
Kyrgios threw up a serve while leading 4-1 in the final set. And she served out with massive yell of emotion towards her supporters.
Vandeweghe said after the match that she was irritated by what she described as excessive celebrating by her Hungarian opponent during their match. "I'm so happy I could win".
There was more drama earlier on the center court and Margaret Court Arena, when second-seeded Caroline Wozniacki and 2008 runner-up Jo-Wilfried Tsonga had to come back from big deficits. After Nadal had gone up by two sets to love, the third turned out to be a non-event with Dzumhur caving in meekly. Because if you want to get to the top you have to play in all conditions. I was like, 'This is my last chance. So, you know, I feel like I transported myself into the TV this year and I'm finding myself on Rod Laver Arena competing. "It was just not a good day for me serving-wise. I was kind of lucky".More news: Putin takes dip in icy Russian lake on Epiphany
Australia has waited 42 years for a new men's champion, so expectations will rise again following Kyrgios's impressive win, a third successive match without a major meltdown for the hot-headed 22-yearold. She clinched a 75-minute third set on her first match point when Fett netted a backhand.
Sixth seed Marin Cilic dispatched Ryan Harrison in straight sets and will meet Pablo Carreno Busta next, while there were also wins for Kyle Edmund and Andreas Seppi as the last 16 started to take shape.
Kostyuk, who had nine double faults Friday, including on match point, received entry into qualifying because of her junior girls' victory previous year at the Australian Open.
It pitches the mercurial Australian into a round of 16 showdown with Bulgaria's world No.3 Grigor Dimitrov on Sunday. Luksika had beaten Belinda Bencic in the second round after Bencic defeated Venus Williams in the first.
The ATP World Tour Finals victor, who won 6-3 4-6 6-4 6-4, said: "I'm not going to give any excuses right now".