Serving for the set, Anisimova struck an ace which she followed up with a forehand volley winner as well as a crosscort forehand winner to hold serve to lead 7-5.
At three games all in set two, Anisimova struck a down the line backhand winner to reach breakpoint.
Osaka hit her seventh doublefault of the match to drop serve and trail 3-4.
Then serving for the set at 5-4 30-0, Anisimova struck a down the line forehand winner to reach matchpoint.
On her third matchpoint of the day, the American hit a down the line backhand winner to hold serve and end the match after one hour, thirty minutes of play.
The match was played mostly with short hardcourt-like points.
In her loss Osaka hit 29 unforced errors to only 13 winners while Anisimova struck 27 winners to 29 unforced errors.