The 35-year-old from Taiwan became the oldest first-time grand slam quarter-finalist in the open era when she upset world No.20 Czech Marketa Vondrousova 6-4 6-2 on Sunday.

Mentored by former Australian Open tournament director Paul McNamee, Hsieh's first quarter-final berth came in her 38th major.

As well as doubles great McNamee, the world No.71 has an Australian fitness coach, massage therapist and hitting partner and has also spent off-seasons in the country.

"I quite like here. I have an Australian coach. Most people know it. This year I have a hitting partner, he's living Melbourne. We have a lot of fun together," Hsieh said.

Hsieh will face 2019 champion Naomi Osaka on Tuesday after Japan's third seed clawed her way to a 4-6 6-4 7-5 win over 2020 finalist Garbine Muguruza.

Watched in the Margaret Court stands by McNamee, the crafty Hsieh unsettled her 21-year-old opponent with her unorthodox game that includes a two-handed forehand.

Vondrousova, the 2019 French Open finalist, put up a fight in the first set but did herself no favours with 31 unforced errors for the match

Hsieh, who upset 2019 US Open winner Bianca Andreescu in the second round, said she was excited to get a straight-sets win.

"It's a bit strange with no crowd but it was great to get the win today," said Hsieh, who is the top-ranked doubles player and doubles No.1 seed in Melbourne with Czech Barbora Strycova.

"I tried to focus on my game and get better in the second because the quarter-final I don't want to miss."

Hsieh reached the Australian Open fourth round in 2018 and 2008 before setting her new high this year.

"So I will be back next year," she laughed before crediting McNamee's influence.

"He don't try to change too much my stuff, but he give me some idea and try to help me to improve my game," Hsieh said.

"I was working with him for years before, so we know how we work together. It's quite comfortable when every time I work with him."

Hsieh could face Serena Williams in the semi-finals if she continues her breakout run.

Williams continued her quest for a record-equalling 24th grand slam singles crown with a 6-4 2-6 6-4 win over Belarusian seventh seed Aryna Sabalenka.

She will next take on two-time major winner Simon Halep, the second seed, who ground out a tough 3-6 6-1 6-4 win over reigning French Open champion Iga Swiatek.

Australian Associated Press