This is coming a year after her dramatic withdrawal from the clay court Grand Slam tournament amid mental health issues.
Up against 27th seed Anisimova, four-time Grand Slam champion Osaka never looked comfortable on her least favourite surface as she struggled to control her powerful game.
The first three games all went against serve in a tense start but Anisimova held to go 3-1 ahead.
A backhand error by Anisimova allowed Osaka to level for 3-3, but a double-fault in the 11th game allowed Anisimova to move 6-5 up and she held serve to love to take the set.
Anisimova broke decisively for 4-3 in the second set as Osaka again double-faulted.
After a couple of match-points went begging, Anisimova finished it off with a stunning backhand winner down the line.
Osaka withdrew from the tournament in 2021 after boycotting post-match media duties for mental health reasons.
In the build-up to last year’s French Open, Osaka said she would not attend the obligatory news conferences for players after matches as they impacted her mental well-being.
The Japanese at that time had revealed she had been suffering from depression for almost three years.
She returned to competitive tennis at the Tokyo Olympics after the saga cast a spotlight on players’ post-match media duties.
Roland Garros organisers conceded they could “do better” on mental health this year.
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