Suarez Navarro, ranked 28th in the world, defeated Francesca Schiavone 6-7 (5-7), 6-4, 6-2 to even her match record this year at 7-7.
She will meet Silvia Soler-Espinosa in one of Friday's semifinal matches. Soler-Espinosa ousted Karin Knapp 6-2, 6-2.
Third-seeded Alize Cornet also advanced by rallying to a 3-6, 7-6 (10-8), 7-6 (7-2) triumph over Lourdes Dominguez Lino.
Cornet will face either No. 1 seed Sara Errani or Kiki Bertens in the semifinals.