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.

Police detain organiser of Messi visit after Indian fans rip up seats
Patel dominates as Mumbai take Game 1 of United Series
UAE though to Arab Cup semi-finals after beating Algeria on penalties
Dubai Basketball claim thrilling win over Bayern Munich in EuroLeague
