The Australian thumped the 119th seed 6-0, 6-1 at Rod Laver Arena to set up a second-round match against Italian Lucia Bronzetti.
Barty won 11 games in succession to begin the match before her opponent had a consolation hold of serve late.
AS IT HAPPENED: Tennis great’s emotional tribute to winning Barty
The Queenslander took just 54 minutes to defeat Tsurenko.
“I don’t think Ash is in any mood for a let-up tonight,” said English tennis icon Sam Smith on Nine’s Wide World of Sports coverage.
Australian tennis great Jelena Dokic was highly impressed with the performance.
“She’s not over-playing, she’s sticking with her tactics, she’s patient,” Dokic said late in the match.
“You’ll never see her really go out there and do something over the top and go for too much.
“That was clinical tonight,” Dokic added during an on-court interview with Barty.
Jelena Dokic’s emotional tribute to Ash Barty
Expectations of a Barty Australian Open title are higher this year after the 25-year-old clinched glory at Wimbledon in 2021.
Barty became the first Australian woman to conquer Wimbledon since Evonne Goolagong Cawley in 1980.
She appears headed for a fourth-round Australian Open showdown with four-time major singles champion Naomi Osaka.
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