Johanna Konta will face Caroline Wozniacki at the Nature Valley Classic after beating Aleksandra Krunic.
Kiki Bertens into the Nuremberg quarters, but Sam Stosur crashed out in Strasbourg.
Heather Watson won her opening match at the Nuremberg Cup.
Sloane Stephens and Madison Keys advanced at the Italian Open on Monday.
Take our 10-question teaser on the career of Dominika Cibulkova.
Maria Sharapova suffered a first-round exit at the hands of Monica Niculescu at the Qatar Open.