A semi-finalist a year ago, Barty had looked set to defeat Shelby Rogers in just an hour but she failed at her first attempt to serve out the match. But she steadied herself to get the job done at the second attempt in a 6-3, 6-4 victory.
It was the sole slip-up in an otherwise flawless performance by the Australian, who missed almost the entire 2020 season because of the Covid-19 pandemic but has not dropped a set in Melbourne to date.
Barty now faces Karolina Muchova after the Czech player edged out two tight sets against Elise Mertens to win 7-6, 7-5.
Afterwards, Barty, who is bidding to become the first female home Australian Open in 43 years, said: “It’s really excited to be through to another quarter-final. If you had told me this would have happened in pre-season, I would have have had a massive smile on my face.
“I just love being at home, I love being in Australia and sharing it with my friends and family. I knew the serve was going to be massive and Shelby is a player who can take the match away from you very quickly so I had to have my running shoes on.”
Jessica Pegula produced the shock of the day in the last 16 of the women’s draw to defeat No5 seed Elina Svitolina 6-3, 3-6, 6-3.
She now faces fellow American and friend Jennifer Brady in the last eight after Brady beate Donna Vekic 7-5, 6-1.