Down three match points, Sevastova swung a forehand away at net to save the first, but Osaka wouldn't be deterred, putting away a searing forehand of her own to clinch her spot in the last eight.
Svitolina beat 17th seed Madison Keys in another three-set match, 6-2, 1-6, 6-1. "I just went in the auto and stuff", she said after winning through to the quarter-finals of the Australian Open on Monday.
Elina Svitolina will take on US Open champion Naomi Osaka in a mouth-watering Australian Open quarter-final after both battled through their respective last-16 clashes. It will be a new experience for whoever wins that showdown, with neither of them going beyond the quarter-finals at Melbourne Park before.
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Osaka had to compose herself at times on court against the dogged Sevastova, who went into the match with a 2-2 record against the 21-year-old. I mean, I was watching him and Tiafoe. "Last night (Stefanos) Tsitsipas beat (Roger) Federer and I was like whoa, and I decided I wanted to do well too", she said of rallying back.
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Osaka also revealed she sometimes now wears a wig when she goes out, especially in Japan. The Ukrainian won their other three matches, two as a front-runner.
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Although Keys won five games in a row, Svitolina was more accurate when it came to winning break points when she managed to fend off five of them until she eventually won in the third set. "I think I believe in myself more this year than I have last year", she said.
"I think that's everyone's dream", she added.
"It was very hard because the sun was burning my eyes when I was tossing the ball". She accomplished the feat for the first time previous year during her championship run at the U.S. Open, where she became the first player of Japanese or Haitian descent to win a Grand Slam.
The victor will play seventh seed Karolina Pliskova, who won the Brisbane International warm-up, or two-time major victor Garbine Muguruza. Meanwhile, fourth seed Alexander Zverev has his work cut out against big-serving Canadian Milos Raonic, with Croat Borna Coric or Frenchman Lucas Pouille awaiting the victor.
Six-time champion Djokovic was taken to four sets by teenage Canadian Denis Shapovalov in the third round and meets another young gun in Russia's Medvedev, seeded 15.