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.
Hazlewood takes six wickets as Australia win first Test
Australia paceman Josh Hazlewood bowled his side to a 214-run victory on the last day of the first Test at Kingsmead on Tuesday with South Africa's resistance ending before tea as the home side were dismissed for 206.
Bethell returns as England name squads for Australia white-ball tour
All-rounder Jacob Bethell has returned from a knee injury after England named their squads for November’s white-ball tour of Australia.
Rwanda to bring F1 back to Africa for first time since 1993
Africa will return to the Formula One calendar for the first time this century with Rwanda agreeing a 10-year deal to host a grand prix from the early 2030s, the sport announced on Tuesday.
Ronaldo on target as Al-Nassr win after security delay
Cristiano Ronaldo has scored Al-Nassr's second goal as the Saudi Pro League champions overcame an hour-long security delay to beat Uzbekistan's Neftchi 3-1 in the AFC Champions League Elite on Monday.
Coventry savour first home Premier League win in 25 years
Coventry City appear to have found their feet in the Premier League after claiming their first home win of the season with a thumping 4-1 victory over Newcastle United on Monday.
Mr Know It All
Teddy Swims
Storm Ii <New>
Gener8Ion & Yung Lean
Stargazing
Myles Smith