No. 3-ranked Grigor Dimitrov did it tough, too, before advancing to the quarterfinals at the expense of the last Aussie in the draw. The actor, producer and comedian was courtside at the Australian Open to see Kyrgios topple Jo-Wilfried Tsonga 7-6 (7-5), 4-6, 7-6 (8-6), 7-6 (7-5) in a Grand Slam classic on Friday.
Dimitrov downed the 17th seeded Kyrgios 7-6 (7/3), 7-6 (7/4), 4-6, 7-6 (7/4) in 3hr 26min and will face Britain's Kyle Edmund in the quarter-finals on Tuesday.
The 22-year-old is showing greater maturity at the Australian Open after frequent criticism in the past for his on-court blow-ups.
"A great battle", Nadal said after finally seeing off Schwartzman. Seppi has been playing very well, but so was I. through to my first quarter-final, I'm really happy.
"That's confidence for myself - knowing that I can resist nearly four hours on court at a good intensity, so quarterfinals already".
After a charmed run of 15 consecutive grand slam matches against players ranked outside the world's top 25, Cilic - runner-up to Roger Federer at Wimbledon past year - will be Nadal's first top-10 challenge at the majors since he beat Stan Wawrinka in the 2017 French Open final.
The lefthander resumed with renewed vigour to break Schwartzman to love and after roaring to 5-2, he claimed the third set with an ace.
The second game of the fourth set lasted nearly 13 minutes and 20 points, with Nadal finally holding after saving five break points. "Of course, I feel little bit exhausted, but I was able to keep fighting until the end".
A former semi-finalist at Melbourne Park, Cilic also equalled Goran Ivanisevic's Croatian record of 11 grand slam quarter-final appearances. That's because I am doing the right things.
Nadal was rattled by a feisty challenge from Schwartzman but held firm to fend off the diminutive Argentine 6-3 6-7 (4) 6-3 6-3 to reach the last-eight of the Australian Open for the 10th time. He's a player that if I don't play my best, probably I am not going to win.
Schwartzman saved 2 break points in game 7, Nadal did the same a few minutes later and Diego had to serve to stay in the match in the 9th game.
She posted a straight-sets win over Croat Petra Martic and will now play either fourth seed Elina Svitolina or Czech qualifier Denisa Allertova.