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.

Luiten leads the way at DP World Tour Championship
Jake Paul hails Dubai as "perfect place" for Christmas Eve comeback fight
Derron and Taylor-Brown renew T100 title fight in Dubai
Racing Bulls confirm Lawson and Lindblad for 2027
Manchester United sack Carrick, talks ongoing for Pochettino
