Pegula, 29, will face her compatriot Madison Keys (17th and 2017 finalist at Flushing Meadows) on Monday for a place in the quarter-finals. She has already reached the quarters in Grand Slams six times, including twice this year (Australia and Wimbledon) and in New York last year, but has never managed to climb into the last four.
Svitolina, wife of French player Gaël Monfils and who gave birth to a baby girl last October, resumed competition in April and had also reached the quarter-finals at Roland-Garros.