Stephens edged fellow American Lauren Davis 6-3, 4-6, 7-5 in 2 hours, 41 minutes. Stephens had eight aces but had to overcome five dropped service games. She managed that by winning seven of her 19 break opportunities, including going 4-for-7 in the third set.
Stephens won 115 points while Davis took 109 on the day.
Mona Barthel, at No. 9 the only other seeded player left in the draw, topped Tsvetana Pironkova 6-3, 6-3 in just 63 minutes. She won 69 percent of the points when serving and 52 percent off Pironkova's serve.
Also Thursday, Kirsten Flipkens dominated the final set in a 2-6, 6-4, 6-0 win over Monica Niculescu and Elena Vesnina defeated Jarmila Gajdosova 6-3, 6-2.
Stephens goes against Vesnina in the first of Friday's semifinals. It will be their first WTA meeting. Flipkens just got by Barthel in their only previous match.
2014: The Year in Music [PHOTOS]