The Australian has had a very up and down year and has dropped outside the top 10 to 19 in the rankings, but she won her second title of 2013 in Osaka last week.
Things did not start well against Ivanovic but from 3-0 down she took control to win 7-5 6-4.
Stosur said on wtatennis.com: "I certainly had a few things in my head today that I wanted to try against her.
"Right from the start it was all kind of working and my confidence started to build, and I was able to play well right through to the end of the match. So I'm pretty happy with how everything went out there."
Next up for the seventh seed is home hope Svetlana Kuznetsova, who knocked out second seed Roberta Vinci 6-2 6-3.
The defeat ended Vinci's hopes of being an alternate for the WTA Championships in Istanbul next week.
The other semi-final will be between fifth seed Simona Halep - who eased past Alisa Kleybanova 6-1 6-1 - and Russia's Anastasia Pavlyuchenkova, a 6-0 6-4 winner over Daniela Hantuchova.
In the men's draw, top seed Richard Gasquet defeated Teymuraz Gabashvili 6-3 6-2 to set up a last-four meeting with 6ft 10in Croatian Ivo Karlovic.
Karlovic ended the run of 17-year-old Karen Khachanov with a 6-4 6-0 victory - the first time the 34-year-old has won a set to love in his 432 matches on the ATP Tour.
Defending champion Andreas Seppi was 5-2 up on Edouard Roger-Vasselin when the Frenchman retired and he faces Mikhail Kukushkin, who won the battle of the Kazakh qualifiers against Andrey Golubev.
Meanwhile, in the doubles, Liverpool brothers Ken and Neal Skupski reached their first ATP Tour final together with a 6-3 5-7 10-7 victory over Russians Victor Baluda and Konstantin Kravchuk.