The Swiss player sailed through the second set without facing a break point and dug in as Stephens attacked in the decider before clinching a 6-7 6-4 7-5 win to move into the semifinals.
Top seed Angelique Kerber sealed her passage into the last four with a 6-3 6-1 win over home player Patricia Mayr-Achleitner to secure her spot at the WTA Championships in Istanbul.
The German was never threatened on serve as she broke her opponent four times to earn a comfortable win.
Spain’s Carla Suarez Navarro also advanced with a 6-1 6-3 win over Wimbledon semi-finalist Kirsten Flipkens.
- Angelique Kerber