World number 35 Zakopalova got off to a slow start in the WTA International clay-court event on Wednesday, dropping her first two service games to fall 3-1 behind in the opener.
However, the Czech then reeled off four consecutive games to take command before serving out to move a set to the good.
Both players started the second set slowly by dropping serve, but Zakopalova turned on the style at 1-1, winning five games on the bounce to ease in to the last eight.
Third seed Paula Ormaechea also progressed in straight sets, as she overcame Kiki Bertens 7-5 7-5.
Ormaechea, ranked number 65 in the world, was broken twice in the first set, but Bertens failed to hold when serving for the set at 5-4 to the good. The Argentinian then held and broke again to take the opener after 77 minutes.
Bertens will rue her collapse in the second set, as she raced into a 5-1 lead before losing six games on the spin - including three on her own serve - to bow out in disappointing fashion.
Ormaechea will meet Nastassja Burnett next, after the Italian came through 0-6 6-3 6-2 against fellow qualifier Alison Van Uytvanck.
Belgian Van Uytvanck got off to a flyer by taking the opening set without dropping a game in just 28 minutes, but Burnett stormed back to seal her place in the quarter-finals.
Fifth seed Kurumi Nara had little trouble dispatching Hsieh Su-Wei 6-3 6-2 in round one, breaking seven times throughout the match.
Poland's Katarzyna Piter, meanwhile, came from a set down to defeat German Dinah Pfizenmaier 5-7 6-3 6-1.
Pfizenmaier knocked out seventh seed Barbora Zahlavova Strycova in round one, and looked on course for a spot in the last eight when she edged a tight opener by breaking when 6-5 up.
However, Piter set her stall out early in the second set by quickly establishing a 3-0 lead before going on win it 6-3 to level matters, before then cruising into a quarter-final meeting with Zakopalova.
Pfizenmaier's compatriot Anna-Lena Friedsam fared better in her first-round clash, though, as she comfortably beat Ukraine's Nadiya Kichenok 6-2 6-3 to book a tie with Nara.