Breaks in the penultimate games of both sets proved decisive as No.2 seed Stephens edged a tight contest, 75 64, to book a quarterfinal meeting with Stefanie Voegele.
"It's tough, she played really well," Stephens said. "She made me play a lot of balls so I had to stay patient and be solid and I think I did a good job of that today.
"I'm a little tired and definitely looking forward to a vacation in the holidays after the season is over. But now I'm just looking to go out with a bang - this year has been awesome and to end it on a good note would be great."
Victory offers Stephens the opportunity to avenge her painful defeat to Voegele six days ago in Linz, where she frittered away a 5-2 final set lead. "Last week wasn't great, but it was close and I just made a few errors at important moments and didn't really stay focused," Stephens added. "This time I'm just going to go out and play my best and hopefully play some good tennis again."
Voegele is one of four unseeded players in the last eight, taking her place there with a 61 36 63 win over Karolina Pliskova.
Among the other surprise names still in contention is Karin Knapp, after she knocked out Andrea Petkovic, 75 75. Following a few years in the wilderness as she came back from first heart and then knee surgery, Knapp is finally beginning to rediscover the sort of form that took her as high as No.35 in 2008.
Now with a clean bill of health, the Italian is back winning and back in the Top 50. Her next test will come in the shape of No.3 seed Sabine Lisicki, who impressed during a 64 60 win over Tereza Smitkova.