Japan’s Osaka, 21, overcame a poor start to beat two-time Grand Slam champion Victoria Azarenka 4-6 7-5 6-3.
Osaka is chasing her third successive Grand Slam title having won the 2018 US Open and the Australian Open earlier this year.
She will play the Czech Republic’s Katerina Siniakova in the next round after she beat Greece’s Maria Sakkari.
“I was lucky enough to play her (Azarenka) twice before this and I knew she was playing really well,” said Osaka.
“It was unfortunate that this was a second-round match but I am happy I won.”
Asked if she is as calm on the inside as she looks on court, she added: “No. I choked on this side (at 5-1) and almost choked on the other side (at 5-3). I am very emotional.”
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