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Osaka had two match points in hand during the deciding set but could not convert them and her American opponent won the subsequent super tiebreak for a 6-4 3-6 7-6 victory.
Osaka is playing in only her second tournament since being knocked out in the US Open and taking a break from the game.
But she showed little ring rust as she deservedly took the opening set. Hopes of carrying that momentum into the second were nullified by former French Open semi-finalist Anisimova, who found her rhythm with her heavy groundstrokes.
She deservedly took the second set and, despite putting repeated pressure on the Osaka serve in the decider, looked in danger of losing the match when facing two break points on her serve.
But she kept her cool to hold and force a tiebreak, which she dominated from the opening point and won 10-5 with an ace.
It set up a potentially thrilling fourth-round encounter against home favourite Ash Barty, who had a far more comfortable passage into the fourth round as she took just a minute over the hour mark to beat No30 seed Camila Giorgi.
The world No1 has spent less than three hours on court in her three matches to date and was again ruthless in dispatching her fellow seed.
“I thought tonight was really clean,” said the Australian afterwards. “I looked after my service games. I was able to keep momentum going, keep making returns.
“I felt like I was out of my weight class the way she hits the ball. All in all, I thought it was pretty good.”
There were no Brits in action on day five of the Australian Open with Dan Evans, the sole Briton left in the main draw, playing tomorrow.
Wimbledon runner-up Matteo Berrettini came through a marathon five-set match against Carlos Alcaraz, winning a final-set tiebreak to beat his teenage opponent 6-2 7-6 4-6 2-6 7-6. Berrettini turned his ankle in the match and needed medical treatment in the final set.
Berrettini looked to be in the ascendancy against his 18-year-old opponent, seen as one of the rising stars of the men’s game, as he moved into a two-set lead before Alcaraz hit back, levelled the match and created a thrilling deciding set.
Afterwards, the Italian said: “He is unbelievable. He is impressive and will only improve playing matches like this. He has shown everyone his potential. Luckily today I won.”
Berrettini was joined in the third round by Alexander Zverev, who had a relatively comfortable 6-3 6-4 6-4 win over qualifier Radu Albot.