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.
Osaka brings the style again to beat Gasanova in Wimbledon second round
Four-times Grand Slam champion Naomi Osaka continued her impressive start to her Wimbledon campaign with a clinical 6-3 6-2 victory over Russian qualifier Anastasia Gasanova to reach the third round on a sunny Wednesday.
First-half goals send Mexico to comfortable 2-0 victory over Ecuador
Julian Quinones delivered a goal and an assist in the first half for Mexico, who maintained complete control in front of their vocal home fans to earn a 2-0 World Cup victory over Ecuador in a round of 32 match on Tuesday at Mexico City.
Mbappe scores twice as France ease past Sweden 3-0 to reach last 16
Kylian Mbappe scored twice as France swept aside Sweden 3-0 in the World Cup round of 32 on Tuesday, maintaining their perfect record of four wins from four and setting up a last-16 meeting with Paraguay.
Serena and Wawrinka go down fighting at Wimbledon
Serena Williams returned to competitive singles action on Tuesday amid huge fanfare after a four-year absence but the American icon could not overcome the first hurdle at Wimbledon and was beaten 6-3 6-7(6) 6-3 by Australian Maya Joint.
Norway edge Ivory Coast to advance at World Cup
Erling Haaland shattered Ivory Coast's World Cup hopes on Tuesday, netting an 86th-minute winner that sent Norway into the last 16 with a 2-1 victory at Dallas Stadium.
