Svitolina saved five break points in the marathon game, with the hold giving her the momentum to streak into a second successive Australian quarter final.
The sixth-seeded Svitolina battled for almost three hours to see off Zhang Shuai in the previous round and showed impressive mental strength again in a tough three-set victory over American Keys. She gave birth to a daughter in September 2017, then sat out last year's Australian Open. "I think we left everything on court", Svitolina said after the match.
"I was happy I could handle the pressure at 1-1 in the third set", Svitolina said.
French Open champion Halep struggled in her opening two matches, where she was extended to 3 sets in both, before finally hitting form to beat Serena's sister Venus in round 3.
"I have been working on [my mindset] for past two years, trying different things, different techniques, and trying to find what works for me".
Sevastova was no stranger to the second week at slams, having reached the semifinals and two quarterfinals at her past three US Opens, but as this battle wore on, it was Osaka whose game was lifting and Sevastova emotionally unravelling.
In Saturday's late action, Lucas Pouille ended the run of 19-year-old wild-card entry Alex Popyrin by holding on to edge him 7-6 (7-3), 6-3, 6-7 (10-12), 4-6, 6-3 in the third round. I don't know how to describe that.
"It was very hard because the sun was burning my eyes when I was tossing the ball".
In her third-round win over Hsieh Su-wei, the 21-year-old Osaka got a warning from the umpire for spiking her racket after losing the first set.
Trailing 3-0, Elina fought back to win five straight games, only to lose serve at 5-4 while serving for the match, adding more fuel to already very dramatic encounter.
She will play the victor of Naomi Osaka v Anastasija Sevastova on Wednesday.
"I walked into the match knowing that she was going to do a lot of odd things, no offence", Osaka said. "So I think her level is good", said Williams' coach, Patrick Mouratoglou.
But Hsieh pounced as the error-rate crept and the normally softly-spoken Osaka became agitated when she conceded three set points, dropping to her haunches as she tried to regain composure.