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.
Real Sociedad beat Atletico Madrid on penalties to win Copa del Rey
Real Sociedad beat Atletico Madrid 4-3 on penalties to win the Copa del Rey on Saturday following a 2-2 draw after extra time, with their goalkeeper Unai Marrero saving two spot kicks in the shootout to help his side win the trophy for the fourth time.
Cunha strike earns Man United hard-fought 1-0 win at Chelsea
Manchester United's Matheus Cunha struck just before halftime to earn a 1-0 victory at luckless Chelsea on Saturday, taking them a big step closer to Champions League football next season.
One driver dead, six injured in Nuerburgring race crash
Racing driver Juha Miettinen has died, and six drivers were injured after an accident at the ADAC 24h Nuerburgring qualifiers on Saturday, organisers said.
Brighton's Rutter denies Tottenham crucial victory with last-gasp strike
Brighton & Hove Albion's Georginio Rutter broke Tottenham Hotspur's hearts with a stoppage-time equaliser to earn his side a 2-2 draw that left the hosts in the Premier League relegation zone on Saturday.
France's Pin becomes first woman to drive a Mercedes F1 car
French driver Doriane Pin, winner of last year's all-female F1 Academy series, has become the first woman to drive a Mercedes Formula One car.
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Didn't We Almost Have It All
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Calling all aspiring runners! Who can be part of the 3F Striders?
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Pinoy Expat Corner
What inspired the establishment of the Filipino senior citizens group here in the UAE?
