Gauff, ranked third and the 2022 runner-up at Roland Garros, defeated the Ukrainian 6-2 6-4.
Gauff was up 5-2 and leading by two breaks in the second set when 30th seed Yastremska saved a break to seal the victory.
In her subsequent service game, American Gauff had to save two more break points before overcoming them to win.
Gauff is vying for a second major singles championship after winning the US Open the previous year.
“It’s important to expect great things from yourself but I’m 20 and I’m hoping to be playing for another 10 years or so,” Gauff stated.
I was more anxious going into the Australian Open’s first few rounds, but right now it’s one match at a time.”
After the Italian, ranked 51st in the world, defeated Russian 17th seed Liudmila Samsonova 7-6 (7-4) 6-2 to get to the fourth round of a major for the first time, Gauff will next play Elisabetta Cocciaretto.
Gauff won the junior French Open championship in 2018, proving that he is a natural on clay.
She got off to a great start against Yastremska, taking the early advantage against a player who, while capable of being threatening, lacked consistency throughout.
Gauff swiftly won the first set and broke the second right away before Yastremska’s more forceful serve came back.
