Osaka was a set and 4-1 down to the tricky Hsieh Su-wei before winning 11 of the last 12 games in a 5-7 6-4 6-1 victory.
Svitolina, who was again watched by boyfriend Gael Monfils, was arguably even closer to the exit door and struggling with a shoulder issue against Zhang Shuai.
The sixth seed trailed 3-0 in the third set before coming back to lead 5-3, failing to serve out the match and then eventually winning 4-6 6-4 7-5 in almost three hours.
Asked what her mindset had been in her on-court interview, Svitolina said: “I’m going to die or win.”
She added later: “This situation when I’m almost about to die, I think, ‘OK, there is an opponent across the net, and also struggling in the same situation, also running the same amount of hours on the court’. So I try to think that way and I’m not alone here in hell.”
Zhang had plenty of opportunities to really put the hammer down but could not quite do it and Svitolina went over to her Chinese opponent after the match to offer some consoling words.
“She’s a very nice person,” said Svitolina, who next faces 17th seed Madison Keys after her victory over last year’s semi-finalist Elise Mertens.
“It’s not only about tennis here. I think it’s very important to be a person and to be open. That’s what I am. It’s not like a big deal for me but, when someone is hurting, it’s normal to help.”
Osaka next faces 13th seed Anastasija Sevastova, who she beat in three sets at the warm-up tournament in Brisbane.
The US Open champion was proud of her response in adversity against Hsieh, saying: “Of course I’m happy with how I fought.
“For me, that’s one of the biggest things I always thought I could improve, because it sort of seems like before I would accept defeat in a way.”
Williams has been in devastating form and she made short work of 18-year-old Dayana Yastremska, winning 6-2 6-1.
The title favourite has dropped just nine games on her way to the fourth round and spent only three hours and six minutes on court in total.
Yastremska grew up idolising Williams, and the American gave her young opponent a hug at the net, telling her: “You did amazing, don’t cry.”
"Don't cry. You did amazing. Don't cry."— SportsCenter (@SportsCenter) January 19, 2019
Serena gave uplifting words to 18-year-old Dayana Yastremska after their match. pic.twitter.com/qHGmlBCSBd
Williams added later: “As she was walking towards the net, I could tell she was quite upset. I kind of liked that. It shows she wasn’t just there to play a good match, she was there to win.
“She wanted to win. That really broke my heart. I think she’s a good talent. It’s good to see that attitude.”
Williams also talked to Yastremska in the locker room after the match about a time violation the Ukrainian teenager received in the second set that the American felt was unfair.
“I didn’t think she deserved the time violation,” said Williams. “I thought that the umpire has to wait until the crowd stops clapping before announcing the score.
“I felt just to keep the match going he was announcing it really fast, which is fine, which is normal, but maybe she wasn’t used to that.
“I told her to definitely look into it so she knows going into the future what to expect. I think it’s important for young players to know the rules so they can always be educated for that. I told her I would look into it as well.”
Stefanos Tsitsipas had to apologise for an expletive-laden rant at the Australian Open as he set up a fourth-round clash with Roger Federer.
Twenty-year-old Tsitsipas is arguably the most exciting young talent in men’s tennis and his meeting with defending champion Federer on Sunday will be one to savour.
But the young Greek also has a temper and, after the umpire decided to replay a set point for Tsitsipas during his clash with Nikoloz Basilashvili at 5-3 in the third set, the 14th seed let rip.
Melbourne’s Greek population have turned out in numbers to support Tsitsipas and his countrywoman Maria Sakkari, and there were a lot of young fans in Margaret Court Arena.
Pressed on his language afterwards, Tsitsipas said: “It was heat of the moment. I said some really bad things. I regret saying them. But I really wanted this really bad.
“At that moment it felt like it was slipping (away). He kind of found comfort and confidence after that. So I was really frustrated. I didn’t quite think what I was saying. I wish I could change that and wouldn’t say that. It’s not the right attitude.”
Among a talented generation, Tsitsipas stands out with his flowing curly locks and flamboyant game, but it is his fighting spirit that is perhaps his greatest asset and he showed it in abundance to beat the dangerous Basilashvili 6-3, 3-6, 7-6 (7), 6-4.
Federer and Tsitsipas have never played a competitive match but they each know what to expect from the other having contested a high-level encounter at the Hopman Cup earlier this month.
Tsitsipas knows he must be prepared not just physically but mentally, saying: “If I thought about it now it’s insane I’m in this position where I can actually play him. It’s really emotional.
“It’s not easy to play these kind of players that you’ve been watching for so long. Mentally you have to be much stronger than any other match.
“For players to beat him, they have to be ready and believe in themselves that they are, their game is great enough to beat such a player.”
So does he believe? “I feel good, I can tell you that,” he added.
Tsitsipas was not born when Federer began his professional career but the 37-year-old continues to make top-level tennis look ridiculously easy and his 6-2, 7-5, 6-2 victory over young American Taylor Fritz, during which his four-year-old son Lenny made a rare appearance, was full of highlight-reel shots.
The third seed is excited to be taking on Tsitsipas, saying: “I’m happy I played against him at the Hopman Cup. I think he played really well there. I actually did, too. I thought it was really high-quality tennis. This is obviously a different type of match.
“I’m happy for him. He’s playing so well, and I’m looking forward to the match-up with him. I like how he mixes up his game and also comes to the net. I think we will see some athletic, attacking tennis being played.”
Grigor Dimitrov continued to take advantage of his favourable draw, beating Italian Thomas Fabbiano 7-6 (5), 6-4, 6-4 to set up a last-16 meeting with America’s Frances Tiafoe.
The 20-year-old was in tears on court after backing up his big victory over Kevin Anderson by coming from two sets to one down to defeat Andreas Seppi.
An ugly war of words within Australian men’s tennis has overshadowed the home country’s achievements on court and shows no sign of dying down yet.
It began on Monday when, after a first-round loss, Tomic accused Hewitt of favouring some players over others and said no-one wanted him as Davis Cup captain.
Hewitt then responded in an incendiary press conference on Thursday, calling Tomic a clown and claiming the 26-year-old had tried to blackmail him and threatened him and his family.
“The threats I’ve received for me and my family, that I’ve had for a year and half now, I don’t think anyone would reach out to a person who speaks like that,” said Hewitt.
Now Tomic has fired back, telling the Herald Sun: “I have never threatened his family. Nice, Lleyton. To think how low of a person you actually (are), and why the Australian public never liked you.
“I got nothing to do with your family and I don’t care what’s wrong with you, you liar.”