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.
Arsenal must improve defensively despite win over Wolves, says Arteta
Arsenal manager Mikel Arteta let rip at his players following their 2-1 Premier League home win over Wolverhampton Wanderers, saying their "horrible defensive habits" made the margin of victory narrower than it should have been.
Dubai Capitals secures thrilling nine-run victory over Abu Dhabi Knight Riders
The Dubai Capitals fended off the Abu Dhabi Knight Riders to secure a nine-run victory at the Zayed Cricket Stadium on Saturday.
Dominant pitching leads Mid East to series saving win over Mumbai
Kazuki Yabuta struck out eight and allowed only four hits and one run in 6.1 innings, and Haru Yoshioka had a perfect 2.2 relief with seven strikeouts, including a Fire Ball strikeout to end the game, to give Mid East Falcons the win 5-1 over Mumbai Cobras and tie the United Series (1-1).
Police detain organiser of Messi visit after Indian fans rip up seats
Lionel Messi's tour of India kicked off chaotically on Saturday as fans threw objects, ripped up seats and invaded the pitch at Kolkata's Salt Lake stadium after the Argentine soccer great made only a brief appearance at a ticketed event.
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