While Osaka showed some stretches of sloppy shotmaking in the first set-she hit 16 unforced errors compared to eight winners-credit Boulter for bold serving under pressure and outplaying the world No. 3.
With Barty now set to face Shelby Rogers, Danielle Collins awaits Williams having impressively defeated third seed Karolina Pliskova 7-6 (7-5) 7-6 (7-3), while Garbine Muguruza overcame Anastasia Pavlyuchenkova 6-1 6-2 to set up a meeting with Kenin.
The Japanese star won the last major of 2020 in NY, arriving for each of her matches at the U.S. Open wearing a face mask bearing the name of a different Black American who had died as result of racial injustice.
Naomi Osaka extended her unbeaten streak to 13 matches and Elina Svitolina reached her sixth quarterfinal in her last seven events at the Gippsland Trophy.
Continuing her quest for a seventh career title, Osaka awaits the victor of Konta vs. Begu. The 2020 US Open victor stated, "I was really nervous coming here.
It just felt like a new experience playing here again after such a long while", Osaka said. "So I'm extremely grateful to be here and I'm exceptionally proud to be an Aussie and just be on this lovely court again", she added. "I sort of had to raise my level, kind of go within myself".
Barty looked like the top-ranked player in the first set, then struggled for a while in a 6-0, 4-6, 6-3 win over No. 52-ranked Marie Bouzkova.
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"I feel like there's a lot of shots that I'm missing", said the world No. 3, who last played competitively at the U.S. Open in September.
Ashleigh Barty has won a rather comfortable opener in Melbourne after she was out of competitions for nearly 1 year.
In her second match after nearly a full year off, Barty started well, but didn't have it all her own way, advancing to the quarterfinals with a 6-0 4-6 6-3 win. "I'm just happy to be out here in any circumstances".
"I always feel nice here in Australia, I feel like everyone welcomes me", said Osaka, who won the Australian Open in 2019.
"A little devastating for me", Kenin said following her 5-7 7-5 6-1 victory over fellow American Jessica Pegula on Wednesday.
World No. 2 Halep, like Williams, bucked the trend of close contests, downing Laura Siegemund 6-2, 6-4 to book her Gippsland last-eight clash with Russia's Ekaterina Alexandrova, who upset French Open champion Iga Swiatek of Poland 6-4, 6-2.
"I'm really happy with both matches, so it's good to be back", said Halep.