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 signs off in tears after one last Argentina master class
Lionel Messi has delivered one last master class in blue and white on Tuesday as Argentina's captain brought the curtain down on his extraordinary 21-year international career by scoring one goal and setting up two others in a 3-0 friendly win over Benin.
Spain rally to beat Croatia, Kane shines for England in Nations League
World champions Spain have recovered to beat Croatia 2-1 on Tuesday, with Mikel Merino scoring twice to extend their unbeaten run to 42 matches and seal a place in the Nations League quarter-finals on the final night of the fourth round of group-stage action.
Saudi Arabia defeat UAE to clinch Gulf Cup title
Saudi Arabia have been crowned Arabian Gulf Cup champions, beating the UAE 2-0 in the final in Jeddah to claim a fourth regional title.
Djokovic wins China Open as de Minaur retires injured
Novak Djokovic won his seventh China Open title after Australia's Alex de Minaur retired with a groin injury during the final on Tuesday.
India crush West Indies in first T20
Captain Shreyas Iyer hit a century as India beat the West Indies by eight wickets in the first Twenty20 of their five-match series in Lucknow on Tuesday.
