Osaka and Barty were pushed to the brink but both avoided early exits at Melbourne Park, where both the Yarra Valley and Gippsland Trophy events are being staged.
It wasn't such good news for Boulter, who couldn't capitalise on a superb start and eventually fell to a three-set defeat against the world No 3 Naomi Osaka in the third round of the Gippsland Trophy.
Ash Barty has showcased her fighting qualities in another pre-Australian Open victory at Melbourne Park. The 2020 US Open victor stated, "I was really nervous coming here".
"I like long matches because I can judge the court and it helps with my fitness". "It's a new year but hopefully, I'll keep playing better." . I sort of had to raise my level, kind of go within myself.
"Actually, in NY, I missed the crowd, but I was able to sort of just focus on tennis", Osaka said recently. Osaka's rhythm was improved and her strokes had dictating powers unlike the first set.
On the bottom half of the draw, defending Australian Open champion Sofia Kenin rallied from a set and a break down to fend off Jessica Pegula 5-7, 7-5, 6-2.
Home favourite Barty, who is hoping to break Australia's 43-year singles title drought at the Open, had a fright in her Yarra Valley match against Marie Bouzkova of the Czech Republic, but recovered to win 6-0, 4-6, 6-3.
"I feel like with the matches I've had, the success I had previous year, helps me", Kenin said.
Osaka is aiming to win her second Australian Open title when the tournament begins next Monday, after being crowned champion in Melbourne two years ago.
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.
Kvitova prevailed in a high-quality first set between two of last year's French Open semifinalists before calling a medical timeout for a foot injury while trailing 1-3 in the second.
"But before that, before this whole pandemic, I could count the times on one finger I've done that", she said.
Barty and Rogers have met once, at the 2017 Australian Open, with Barty claiming a 7-5 6-1 second round victory.
Eighth seed Evans beat Portugal's Pedro Sousa 6-3 7-5 in the second round of the Murray River Open, having received a bye in the first round. Svitolina streaked through 10 straight points stamping a love break for a 3-0 lead in the final set closing in two hours, 12 minutes for her sixth quarterfinal in her last seven tournaments.
"It was a really solid match". Players like Serena Williams, Novak Djokovic, and Rafael Nadal were part of that event too.