Sevastova toppled seventh-seeded Elina Svitolina 6-3, 1-6, 6-0, leaving just two of the top 10 women’s seeds remaining.
Stephens, runner-up to Halep at the French Open, was looking forward to taking on Sevastova again in her bid to push ahead in her title defense.
“Obviously it won’t be easy,” she said. “Quarter-finals of a Grand Slam is always really tough. A big opportunity for both of us. Being defending champion, being able to get to the quarter-finals again, is incredible. I’m just going to try to keep building on that and keep going.”
Sevastova, in the quarters for a third straight year, is hoping to turn the tables on Stephens, who is trying to become the first woman to win back-to-back US Open titles since Williams won three straight in 2012, 2013 and 2014.
“Maybe third time lucky for me,” Sevastova said.