The top-seeded Pole broke Cirstea six times, a day after being forced to save three match points in a lengthy three-set win over Chinese wild-card entry Duan Ying-ying.
Radwanska will next face Alison Riske of the United States, the player she beat in last year’s final. Riske advanced by beating Tsvetlana Pironkova on Bulgaria 6-1, 6-1.
Third-seeded Johanna Konta also reached the quarterfinals after rallying to beat Vania King 1-6, 6-3, 6-2, while Wang Qiang defeated seventh-seeded Monica Niculescu 7-6 (1), 6-4.
Original author: Ashley Ndebele