The third seed Kirsten Flipkens also progressed to the quarter-finals with a straight sets win over the 21-year-old Czech Karolina Pliskova.
The 27-year-old Belgian, who's ranked 20th in the world, was leading 5-0 in the first set before withstanding a fightback from the Czech to close out the match 6-4 6-3.
Flipkens also made the quarters of the Classic in 2013, before losing to compatriot Yanina Wickmayer.
She reached the semi-finals at Wimbledon last year, where she lost to the eventual champion Marion Bartoli.
Also through on day three is American Jamie Hampton, who beat Pliskova's twin sister Kristyna 6-3 6-4.
