"You can't expect easy matches when you're playing in big tournaments", the world number one told reporters after saving all his seven break points in the final set.
"I played really well from being down 5-1", she said.
Nadal was out in front early with a set and a break but the diminutive Argentine kept pushing and pushing the action.
Carreno Busta showed heart to rally from a break down in the fourth set and push the match into a third tiebreak but was quickly overwhelmed by Cilic's firepower as the Croatian brought up four match points in a hurry.
In an often breathtaking clash boasting some sumptuous shot-making, the Spaniard was stunned by the hard-hitting Schwartzman who broke him three times before claiming the second set at Rod Laver Arena.
With this victory, Nadal secured the ATP ranking's top spot after the tournament, regardless of his results.
The unseeded Edmund, ranked 49, dropped the opening set, but finished strongly to win 6-7 (4/7), 7-5, 6-2, 6-3 and will face world No 3 Grigor Dimitrov in the last eight.
The top seed raced through the match in just 1hr 50min, wasting as little energy as possible in the 6-1, 6-3, 6-1 rout.
New NBA All-Star Game format provides intrigue
From there, the rest of the two rosters will be filled out by the 14 reserves yet to be named, seven each from the East and West. The captains will be the All-Star starter from each conference who receives the most fan votes in his conference.
"But I played with determination, and that's what I'm going to need, and I'm going to need to serve well".
Second seed Wozniacki has not impressed so far, but she put in a better performance to beat Dutch 30th seed Kiki Bertens 6-4, 6-3, finally getting over the line on her fourth match point.
The player who seems most likely to go all the way and lift the title is Svitolina.
Nadal had lost his only previous meeting against Dzumhur, when he had to retire because of heat-related issues in the third set in 2016 at Miami.
The TV favourite sat on the same on-court seats as fellow celebrities Will Ferrell and Will Smith and watched Rafael Nadal do battle with Diego Schwartzman at the Rod Laver Arena.
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.
"My opinion [is] that [it] is not safe enough sometimes, you know?"
"When I saw him out here, I was so nervous, no joke", Kyrgios said. "I feel like my level is there", Kyrgios said. Kyrgios said he's doing nothing special to change his image: "It's not something I wake up and I'm like, "Look, today I'm going to try to change the perception". If he is in a good mood, the chances are he might be able to win. Paes and Raja suffered a straight-set defeat at the hands of the Colombian pair of Juan Sebastian Cabal and Robert Farah 1-6, 2-6.