Former champion Svetlana Kuznetsova had to come from a set down to beat Japan's Ai Sugiyama 1-6 6-1 6-2 and reach the Eastbourne International last eight.
Kuznetsova lost in the final of the French Open earlier this month
The Russian fourth seed, who received a first-round bye, looked rusty early on but eventually found her rhythm.
The French Open finalist said: "It was so windy in the first two games. I got broken and she got confident."
British wildcard Anne Keothavong, 22, bowed out in round one, losing 6-1 6-3 to Russian 19-year-old Vera Dushevina.
Fifth seed Anastasia Myskina made short work of Slovak qualifier Jarmila Gajdosova, the Russian winning 6-3 6-0 to ease into round two.
Belgian duo Kim Clijsters and Justine Henin-Hardenne, the French Open champion, enter the tournament in the second round on Wednesday, along with France's Amelie Mauresmo.