Top-seeded Sara Errani fell to Russia's Ekaterina Makarova 7-5, 6-1 on Wednesday at the New Haven Open.
Errani, ranked No. 5 in the world, became the fifth of the tournament's eight seeds to lose in the first two rounds of the final WTA tuneup before next week's U.S. Open.
"The good thing is that if you lose, you have more time to prepare there, if not, you have more confidence," Errani said. "I hope the court there will be different."
Sloane Stephens, ranked 17th in the world and aiming for her first WTA tournament title, moved into the quarterfinals with a 7-5, 2-6, 6-1 victory over Germany's Julia Georges.
After being dominated in the second set, the 20-year-old Stephens won the next four games and cruised to the win.
"I think me being able to go out and play a third set strong like that is the difference between me today and a year ago," Stephens said. "I just think that I'm at a point where I go out there and I'm (thinking), 'I'm going to win.'"
She is one of just three seeded players to advance past the second round. The others are defending champion Petra Kvidova, who beat American qualifier Alison Riske 7-6 (5), 4-6, 6-3; and four-time champion Caroline Wozniacki, who turned back Italy's Karin Knapp 6-1, 7-5.
Stephens and Wozniacki, who has won the event four of the last five years, will meet in the quarterfinals on Thursday.
But Stephens said she isn't feeling much pressure, despite knowing she will come into that match and next week's U.S. Open with the label of the star-in-waiting for U.S. tennis.
"You kind of have to go with it and accept the responsibility, or whatever you might call it," she said. "But I think, in all, it's a good thing."
Kvitova found herself in a back-and-forth match with the 23-year-old Riske, before breaking her at love in the fifth game of the final set.
"After dropping the second set, it was quite tough to come back in the third. But I'm glad for it, I'm sure," she said.
Errani didn't make it through her first match of the tournament, after receiving a bye in the first round. She had trouble with her slow, spinning serves all afternoon on what she said was a faster-than expected court. She was broken four times by Makarova.
The 25-year-old Russian dominated her own service games, was broken just once and had eight aces.
Makarova will play Simona Halep in the quarterfinals.
Halep didn't have a WTA title before this year, but has three this summer and is 28-5 in her last 33 matches. She dropped her first set Wednesday but bounced back for a 3-6, 6-4, 6-1 win over Carla Suarez Navarro of Spain.