Two-time Wimbledon champion Petra Kvitova and former world number one Caroline Wozniacki made Eastbourne's third round with straight-set wins.
Czech fifth seed Kvitova saw off Hungary's Timea Babos 6-4 7-6 (7-5).
Denmark's Wozniacki - now ranked 37th in the world - produced a superb performance to beat Australian Sam Stosur 6-2 6-1.
British number one Johanna Konta will meet Kvitova in the last 16 if she beats Lesia Tsurenko later on Tuesday.
Polish top seed Agnieszka Radwanska advanced after Mirjana Lucic-Baroni of Crotia was forced to retire from their match by illness while trailing 6-4 2-1.