The US Open champion had a topsy-turvy third-round at the Australian Open on Saturday, getting within two games of elimination before finding her range against a tricky Hsieh Su-wei and winning 5-7, 6-4, 6-1.
Madison Keys had a great day at the office, taking down the 12th seed Elise Mertens 6-3, 6-2 in 73 minutes after 31 winners and 21 unforced errors she hit, losing serve just once and scoring four breaks on the other side to enter the fourth round for the fourth time in five years.
Svitolina was wobbling but the tenacious base-liner dug deep to save five break points in a marathon third game of the decider lasting more than 16 minutes, the vital hold giving her the impetus to kick on for victory.
Serena Williams crushed Ukrainian teenager Dayana Yastremska 6-2, 6-1 before consoling her at the net as she burst into tears.
This contrasts with the massively experienced Serena Williams who has made the last 8 or better 11 times on her way to 7 Australian Open crowns.
"I was happy I could handle the pressure at 1-1 in the third set", Svitolina said.
The second set started badly for Osaka when she conceded an early break and then continued to struggle as Hsieh zipped around the court making stunning returns.
"I have been working on [my mindset] for past two years, trying different things, different techniques, and trying to find what works for me".
Naomi Osaka has come from behind to reach the Australian Open quarter-finals.
Svitolina was a quarter-finalist at Melbourne Park previous year and has made the last eight at Roland Garros twice but is yet to progress further in a Grand Slam. "I didn't know what to do at a certain point but I just stuck in there".
"I walked into the match knowing that she was going to do a lot of odd things, no offense", Osaka said.
Osaka, who faces Latvian 13th seed Anastasija Sevastova next, said she found it hard to settle veteran world number 27 Hsieh's dizzying mix of drop shots and slices.
Sevastova surrendered her serve straight away, however, and Osaka then survived eight deuces in the eighth game before seeing it out two games later.
"I'm happy with how I fought", Osaka said.