Bertens ousted fourth-seeded Dominika Cibulkova 7-5, 6-4, dropping her serve just once and winning two-thirds of the points on serve. The late break in the first set gave Bertens the lead and she had two more breaks in the second set.
Suarez Navarro beat No. 8-seeded Klara Zakopalova 6-4, 6-3 with three breaks in each set. Winning 57 percent of the points off Zakopalova's serve allowed Suarez Navarro to survive dropping four service games.
Top-seeded Sara Errani won the first four games of her match when Magdalena Rybarikova retired.
No. 6-seeded Lucie Safarova took a 6-2, 4-6, 6-2 decision over Alize Cornet. Safarova had two breaks in each set but didn't lose her own serve in the first or third sets.
Kristina Mladenovic finished the second round with a 6-4, 6-4 win over Yanina Wickmayer.
Friday's quarterfinals have Errani playing Suarez Navarro while Bertens takes on Safarova. Also, second-seeded Petra Kvitova goes against Mladenovic and third-seeded Marion Bartoli meets Mona Barthel.