Rain washed out Friday's action completely, forcing officials to schedule both the quarterfinals and semifinals for Saturday. Only the quarterfinals were completed Saturday because of more inclement weather.
The top-seeded Stosur cruised past South Africa's Chanelle Scheepers, 6-2, 6-3, while the second-seeded Bartoli thumped Japanese crowd favorite Ayumi Morita, 6-2, 6-1.
Stosur, the reigning U.S. Open champ, won this event for her first career WTA title two years ago. She will face China's Zheng Jie in the semifinals. Zheng upended fourth-seeded Petra Cetkovska of the Czech Republic, 0-6, 7-5, 6-3, on Saturday.
Bartoli is trying to qualify for the season-ending WTA Championships and will face Germany's Angelique Kerber in the semifinals. The third seed advanced Saturday with a 6-3, 6-4 win over 2010 Osaka champ Tamarine Tanasugarn of Thailand.
This week's champion will take home $37,000.