Osaka dominated her highly rated opponent and carved out a 6-4, 6-4 victory here on Wednesday, reports Efe news agency.
Osaka will now play World No.31 Agnieszka Radwanska in the next round.
"I'm really proud of myself. The biggest thing (in the pros) is about being tougher mentally. I try to take things one point at a time," Anisimova told the Tennis Channel.
In a marathon battle spanning two hours and 23 minutes, Switzerland's Belinda Bencic knocked out Timea Babos 1-6, 6-1, 7-6 to set up a second-round clash with Jelena Ostapenko while Sachia Vickery beat Canada's Eugenie Bouchard 6-3, 6-4.
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