Kyrgios defeated Jo Wilfried-Tsonga in the third round and was mostly well-behaved, a far cry from some of the antics he has pulled in the past, including a suspension in October 2016 for not trying during a match in Shanghai, and a heavily-criticized on-court exchange with Stan Wawrinka in 2015.
The Russian star who missed the Australian Open previous year because of a doping suspension, cruised past Latvian 14th seed Anastasija Sevastova 6-1 7-6 (4) at Rod Laver Arena.
In another match, third seed Grigor Dimitrov survived a tricky test in fierce heat against feisty young Russian Andrey Rublev to reach the fourth round.
On the women's side, Jelena Ostapekno lost to Anett Kontaveit 6-3, 1-6, 6-3.
"It was just not a good day for me serving-wise".
Kyrgios earned a momentous win in his own career as he claimed a four-set victory over childhood hero Tsonga - a man whose autograph he chased as a 12-year-old.
"I started to feel dizzy".
"I've seen him play a lot", he said.
Dimitrov, now 26, has got closest with his trip to the last four at Wimbledon in 2014 and his part in a thriller of a Melbourne Park semi-final against Nadal a year ago.
Petra Martic celebrated her 27th birthday with a 6-3, 3-6, 7-5 over Thai qualifier Luksika Kumkhum.
The 33-year-old Seppi clinched the match with a break of the 38-year-old Karlovic's service, only his second break of nine attempts during the match.
"I don't know if it's elite", he said.
Briton Johanna Konta, ranked 10th in the world, crashed out to world number 123 Bernarda Pera in the second round, with the American winning 6-4 7-5 defeat.
Caroline Wozniacki advanced over Kiki Bertens 6-4, 6-3 after she was pushed to her limit in the round of 64.
Another Ukrainian, Kateryna Bondarenko, beat No. 15-seeded Anastasia Pavlyuchenkova 6-2, 6-3 and will next play No. 19 Magdalena Rybarikova.
"I was very focused and I'm very happy to have another chance on Sunday", Nadal said.
Ryan Harrison beat No. 31 Pablo Cuevas 6-4, 7-6 (5), 6-4 and Kyle Edmund had a straight-sets win over Denis Istomin - who beat then defending-champion Novak Djokovic in the second round here a year ago.
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