The sixth-seeded Stephens is looking for her first WTA Tour win. She is one of only three seeded players to make it out of the second round at Yale, the final tour stop before next week's U.S. Open.
Defending champion Petra Kvitova also needed three sets to get past another American, qualifier Alison Riske, 7-6 (5), 4-6, 6-3. And four-time champion Caroline Wozniacki advanced, beating Italy's Karin Knapp 6-1, 7-5.
Top-seeded Sara Errani fell earlier to Russia's Ekaterina Makarova 7-5, 6-1. Errani said winning would have boosted her confidence, but the loss will give her more time in New York to prepare for next week.