Number four seed Carla Suarez Navarro moved into the quarter-finals of the Internationaux de Strasbourg with a straight sets win over American Christina McHale.
After top seed Caroline Wozniacki withdrew on Monday because of back trouble and number two seed Elena Vesnina then lost her first-round match to qualifier Camila Giorgi, the Spanish world number 22 produced a composed display to see off McHale 6-4 6-1 in one hour and 28 minutes.
Australian Samantha Stosur secured her place in the last eight and a date with Suarez Navarro after she beat Madison Brengle of the United States 6-0 6-1.
China's eighth seed Shuai Peng defeated Frenchwoman Amandine Hesse 7-5 6-2 but Puerto Rican ninth seed Monica Puig is out following her 6-2 6-3 loss against Czech player Kristyna Pliskova.
At the Versicherungs Cup in Nuremberg, both top seeds Kiki Bertens and Yulia Putintseva progressed into the second round.
Bertens saw off Germany's Katharina Gerlach 6-2 6-1 while Putintseva came through 6-4 5-7 6-0 against Julia Glushko.
Number four seed Laura Siegemund beat fellow German Katharina Hobgarski 6-0 6-1.
In Tuesday's second round matches, fifth seed Alison Riske progressed to quarter-finals as the American defeated Belgium's Kirsten Flipkens 6-2 6-2 to set up a potential showdown with Bertens.
Sorana Cirstea battled past Varvara Lepchenko 6-0 6-7 (4/7) 6-3 and could meet Putintseva if she also goes on to reach the last eight.
