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.
Hakimi hat-trick leads PSG to win at Le Havre
Flying fullback Achraf Hakimi grabbed a hat-trick as Paris St Germain went on the rampage to thrash bottom-placed Le Havre 5-1 and extend their Ligue 1 lead on Friday.
Ferrari's Leclerc fastest in both Mexico practice sessions
Ferrari's Charles Leclerc was fastest in both practice sessions on Friday for a Mexico City Grand Prix set to crown 20-year-old Mercedes driver Kimi Antonelli as Formula One's youngest champion.
Bhanwala becomes first Indian woman to win wrestling world title
India's Manisha Bhanwala became the country's first women's wrestling world champion after fighting back from 6-0 down to beat American Abigail Nette 8-6 in the 59kg freestyle final at the World Wrestling Championships in Astana on Friday.
South Africa set Australia 288 to win series decider
Ryan Rickelton and Wiaan Mulder struck centuries as South Africa were bowled out for 387 to close day four of the decisive third test against Australia on Friday, setting the touring side a victory target of 288 on the final day.
Phillips fireworks secure New Zealand's consolation win over India
New Zealand's Glenn Phillips lashed an incendiary 107 to secure a comprehensive 87-run consolation win over India in the fourth Twenty20 International on Friday.
