The No. 2 seed, who made her season debut at an exhibition event in Adelaide last week, needed just under 70 minutes to serve out the French veteran on Margaret Court Arena.
"It felt really nice. I just want to say it felt really good to play in front of people," Osaka said, thanking the crowd for watching.
Osaka ended a pandemic-impacted 2020 season with a third Grand Slam victory and a second in Flushing Meadows. Her 2019 Australian Open run helped her ascend to the top of the WTA rankings for the first time in her career, making her one to watch whenever she plays Down Under.
"I was really nervous coming here," she admitted during her on-court interview. "The last match I played was the finals in New York, and I really wanted to continue that momentum. It's a new year but hopefully, I'll keep playing better."
Playing Cornet, who peaked at No. 11 back in 2009 after a fourth-round run at the Australian Open, the 23-year-old Japanese star breezed through the opening set and navigated through a pair of tough service games to close out the match with 19 winners to 23 unforced errors and a perfect four-for-four break point conversion rate.
"I always feel really nice here in Australia. I feel like everyone really welcomes me, and I'm really glad that you guys opened your arms so we're able to play here."
While Osaka will return to take on Briton Katie Boulter, who pulled off a dramatic comeback against American Coco Gauff, on-fire No. 4 seed Aryna Sabalenka saw her 15-match winning streak end at the hands of Kaia Kanepi, 6-1, 2-6, 6-1.
Like Osaka, Sabalenka ended 2020 undefeated, winning back-to-back titles in Ostrava and Linz, and began the new year with a third title in Abu Dhabi.
Regardless of ranking, the former No. 15 Kanepi has tended put down her best performances on the game's biggest stages, reaching six Grand Slam quarterfinals in her career. Looking in-shape and ready for an upset, the 35-year-old Estonian won the first five games of the match and weathered a second-set fight-back from Sabalenka to surge through the decider and book a third round clash with Daria Kasatkina.
A former world No. 10, the young Russian scored an upset of her own against No. 15 seed Polona Hercog to advance, 6-4, 6-3.
In a thrilling Yarra Valley Classic night cap, No. 4 seed Petra Kvitova held off Venus Williams, 7-6 (6), 7-5, in her first appearance of the New Year. Kvitova finished with 41 winners to 39 unforced errors, compared to the American's 22 to 19 ratio.
Williams wiped away a break deficit in the second set from 1-4 down, but the left-hander dug in by denying the 40-year-old a shot at tie-break redemption. With the two-hour win, Kvitova moved to 5-3 against Williams and scored the first straight-set victory of their head-to-head series.
For a place in the quarterfinals, Kvitova will meet fellow 2020 Roland Garros semifinalist Nadia Podoroska.