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.
Alcaraz stunned by Korda at Miami Open
World number one Carlos Alcaraz was stunned by Sebastian Korda 6-3 5-7 6-4 in the third round of the Miami Open on Sunday, giving the American the biggest win of his career.
Former All Blacks assistant McLeod named Wallabies defence coach
Former All Blacks assistant coach Scott McLeod has been named Wallabies defence coach under incoming boss Les Kiss, Rugby Australia said on Monday.
10-man Real Madrid edge Atletico in pulsating derby
Vinicius Jr scored twice as Real Madrid fought back to beat Atletico Madrid 3-2 in a breathless Spanish capital derby on Sunday, keeping Alvaro Arbeloa's side within four points of LaLiga leaders Barcelona.
Man City win League Cup with O'Reilly double
Two second-half headers by Manchester City's Nico O'Reilly settled the English season's first silverware on Sunday as Pep Guardiola's side beat Arsenal 2-0 in the League Cup final.
Bezzecchi dominates MotoGP Brazil for fourth straight victory
Aprilia's Marco Bezzecchi cruised to victory at the MotoGP Brazilian Grand Prix on Sunday for his fourth consecutive Grand Prix win and now leads the championship standings.
