Barty was playing her first competitive match for nearly a year, having decided to stay at home in Australia when the WTA Tour resumed last summer following a coronavirus-enforced suspension.
Barty, 24, is the top seed in the Yarra Valley Classic and recorded a comfortable 6-3 6-3 win over Ana Bogdan in front of a surprisingly sparse crowd at Melbourne Park.
“I think overall I felt pretty good,” Barty said. “Ana did an exceptional job in making me play to a very high standard. I knew right from the first point I was going to have to be ready tonight and switched on straightaway. That was really nice to have that challenge.”
Petra Kvitova won a high-quality contest to end the day, beating 40-year-old Venus Williams 7-6 (6) 7-5, while sixth seed Garbine Muguruza thumped Alison Van Uytvanck 6-2 6-0.
Australian Open champion Sofia Kenin had just won the first set 7-5 against Camila Giorgi when the Italian retired.
Osaka was playing her first match since lifting her third Grand Slam title last September and eased past Alize Cornet 6-2 6-2 at the Gippsland Trophy.
The Japanese second seed said: “I was definitely really nervous going into it. But I’m really happy with how positive I was throughout the match.”
In the third round Osaka will face Britain’s Katie Boulter, who upset Coco Gauff 3-6 7-5 6-2.
French Open champion Iga Swiatek was playing her first match as a Slam winner and made a nervous start against Kaja Juvan but recovered to win 2-6 6-2 6-1.
Fifth seed Johanna Konta eased to a 6-2 6-3 win over Bernarda Pera but fourth seed Aryna Sabalenka, who was on a 15-match winning streak, was surprisingly beaten 6-1 2-6 6-1 by Kaia Kanepi.
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