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.
Messi becomes first to win MLS Golden Boot in consecutive seasons
Inter Miami's Lionel Messi became the first to win MLS' Golden Boot in back-to-back seasons, the league said on Saturday, the final day of the regular season.
Norris on pole in rain-hit Brazil for third year in a row
Lando Norris has put his McLaren on pole position for the third year in a row at the Sao Paulo Formula One Grand Prix on Saturday in tough conditions after a long delay caused by torrential rain at Interlagos.
Real Madrid sweep aside Valencia to move level with Barcelona
Real Madrid cruised to a 3-0 win at struggling Valencia in LaLiga on Saturday as Federico Valverde, Arda Guler and Kylian Mbappe scored to move the visitors level with leaders Barcelona.
Rybakina pulls out of WTA Finals due to fitness concerns
World number one Elena Rybakina has withdrawn from the WTA Finals, the Kazakh said on Saturday, citing concerns over her fitness.
Egypt part ways with coach Hassan, Maher to replace him
Egypt have parted ways with coach Hossam Hassan, with Ali Maher named as his replacement, the Egyptian Football Association (EFA) said on Saturday.
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