Spain's Suarez Navarro moved on with a 4-6, 6-0, 4-1 (retired) win over defending Florianopolis champ Monica Niculescu when the No. 5 seed exited.
Romania's Niculescu had been broken in five straight service games before retiring from the match.
Suarez Navarro will take on Zakopalova in the semis after the third-seeded Czech also won in a walkover. She was ahead 6-3, 5-2 when Romanian qualifier Alexandra Dulgheru threw in the towel.
Also advancing were second-seeded Garbine Muguruza of Spain, who got past qualifier Alison Van Uytvanck 6-2, 6-7 (1-7), 6-3, and Kazakhstan's Yaroslava Shvedova, winner of a 6-3, 6-3 decision over No. 6 Alexandra Cadantu of Romania.