The World number one beat Croatian Donna Vekic 6-3 4-6 7-6 (7-4) at the Porsche Tennis Grand Prix.
Osaka will now face Anett Kontaveit, who was able to progress after Victoria Azarenka retired.
Petra Kvitova will face Kiki Bertens in the other semi-final.
Australia get Head boost, India ponder Rohit switch for 4th test
In-form Australian batter Travis Head will be fit for the fourth test and India are considering restoring captain Rohit Sharma to the opener's slot for the match starting in Melbourne on Thursday.
Kuwait triumphs over UAE in Arabian Gulf Cup
Kuwait secured a 2-1 victory over the UAE in the second round of the Arabian Gulf Football Cup, also known as "Khaleeji Zain 26," held at Jaber Al-Ahmad International Stadium on Tuesday evening.
Champions Trophy fixtures confirmed, Dubai to host India matches
The ICC Champions Trophy kicks off on February 19 in Karachi and wraps up with the final on March 9, featuring a total of 15 matches across Pakistan and Dubai.
Teenager Konstas to make debut in fourth test against India
Teenager Sam Konstas will make his test debut in the cauldron of the Boxing Day test at Melbourne Cricket Ground on Thursday as Australia look to take the game to India's bowlers, coach Andrew McDonald said on Tuesday.
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