Japan's Osaka, 24, was beaten 4-6 6-3 7-6 (10-5) at Melbourne Park.
Unseeded Anisimova, 20, will play Australian top seed Ashleigh Barty in the last 16.
Barty has still not dropped a set this week after a 6-2 6-3 victory over Italy's Camila Giorgi.
The 25-year-old Queenslander is carrying the hopes of a nation desperate to see a home Australian Open champion for the first time since Chris O'Neil in 1978.
Most expected Barty to face Osaka in the last 16 when the draw pitted two of the game's biggest stars in the same section.