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, Mbappe have moved on from China controversy, says Mourinho
Real Madrid manager Jose Mourinho said on Saturday that the club and Kylian Mbappe had responded appropriately by apologising for the France captain referring to former Chinese leader Mao Zedong as a dictator.
Alcaraz reaches first Vienna final, De Minaur upsets Zverev
Carlos Alcaraz defeated Daniil Medvedev 6-4 7-6(2) on Saturday to reach the Vienna Open final for the first time, with the Spaniard joined by Australian Alex de Minaur who upset Alexander Zverev.
Pressure piles on Man United's Carrick after 2-0 defeat at Chelsea
Pressure intensified on beleaguered Manchester United manager Michael Carrick after his side finished with 10 men in a 2-0 Premier League defeat at Chelsea on Saturday to record their ninth straight game without a win in all competitions.
Harmer, Rabada steer South Africa to series win over Australia
South Africa spinner Simon Harmer took a career-best 6-16 and Kagiso Rabada became the fastest by balls bowled to reach 350 test wickets as the hosts thumped Australia by 176 runs to clinch their three-match series 2-1 at Newlands on Saturday.
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.
