Safarova defeated second-seeded Caroline Wozniacki in a second-round match Wednesday and took out No. 14-seeded Svetlana Kuznetsova 7-6 (8-6), 6-3 Thursday in advancing to the tournament quarterfinals.
Kuznetsova fought off five break points in the first set but Safarova was able to take the tiebreaker. Safarova notched a pair of breaks in the second set to win.
Azarenka improved to 14-0 on the year with a 6-3, 6-1 win over Simona Halep. Azarenka piled up six breaks over Halep's eight service games.
No. 3-seeded Samantha Stosur topped Petra Cetkovska 6-3, 6-2 with five breaks while fourth-seeded Agnieszka Radwanska beat Varvara Lepchenko 7-5, 6-1 and Marion Bartoli, the No. 5 seed, got by Tsvetana Pironkova 6-3, 6-3.
Also Thursday, Yanina Wickmayer was a 6-4, 6-0 winner over Ksenia Pervak, Christina McHale rallied for a 4-6, 6-3, 6-4 decision over Shahar Peer, and Monica Niculescu advanced at the expense of Kateryna Bondarenko 7-6 (7-5), 6-4.
Azarenka plays Wickmayer and Radwanska goes against McHale in one half of the draw's quarterfinals while Stosur faces Niculescu and Bartoli meets Safarova in the other.
Notable deaths of 2014 [PHOTOS]