The fourth seed, who reached the semi-finals in Mallorca last week having beaten Maria Sharapova, will face Sweden's Rebecca Peterson next after she beat Lesia Tsurenko.
Former world number one Simona Halep was impressive as she opened her Eastbourne campaign by thrashing tricky Taiwanese Hsieh Su-Wei 6-2 6-0 in less than an hour.
"It felt really well because I played great tonight, and I felt the ball a lot," Halep, who faces Polona Hercog next, said.
In the match of the day Latvia's former French Open champion Jelena Ostapenko, a semi-finalist at Wimbledon last year, beat American Sloane Stephens 1-6 6-0 6-3 in a topsy-turvy match.
Home favourite Johanna Konta moved into the last 16 by beating Greece's Maria Sakkari 6-4 7-6(4).
The world number 19 will now face Tunisia's Ons Jabeur.
Dutchwoman Kiki Bertens, seeded three, also posted a solid win, beating Kazakhstan's Yulia Putintseva 6-4 6-1.
In the ATP tournament former world number one Andy Murray's unbeaten start to his comeback from hip surgery ended as he and Brazil's Marcelo Melo lost 6-2 6-4 to Colombian top seeds Robert Farah and Juan Sebastian Cabal.
Murray had beaten the same pair last week playing with Spain's Feliciano Lopez on the way to the Queen's Club title.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
