The Czech star beat Estonia's Anett Kontaveit 6-3, 7-6 (7/2) in the final, succeeding compatriot Karolina Pliskova as champion at the clay-court event.
The 21-year-old Japanese was scheduled to play a semi-final tie against Estonian eighth seed Anett Kontaveit
Osaka said that she had tried to "think logically" when she found herself on the brink of defeat in Friday's quarter-final.
US and Australian Open champion Osaka secured a place in the quarter-finals against Croatia's Donna Vekic.
Osaka said that winning was not everything in Stuttgart, where she last played as a qualifier in 2017.
Dortmund opened a nine-point gap by mauling second-from-bottom Hanover 5-1 on Saturday, but defending champions Bayern trimmed the lead back to six.
The staff, taken out by the security staff in airports at Duesseldorf, Cologne-Bonn and Stuttgart affected around 100,000 passengers.
Pavard has been at struggling VfB Stuttgart, who are currently third from bottom in Germany's top flight, since 2016 after he joined from French side Lille for five million euros.
After back-to-back league defeats, Bayern leapt from sixth to second in the Bundesliga behind Borussia Dortmund who routed Stuttgart 4-0
The Germany international had several chances in a hard-fought first half, eventually curling the ball into the bottom corner on 37 minutes.
After serving a 15-month drugs ban for use of the illegal heart medication meldonium, Sharapova's return to the WTA circuit began in Stuttgart exactly a year ago.
Gomez’s first-half strike was enough to secure a first away win of the season for Stuttgart, and inflict a home defeat on Augsburg since October.
Borussia Dortmund suffered another setback in their bid to challenge for the Bundesliga title as they lost 2-1 at VfB Stuttgart on Friday.