Seventh seed Zakopalova has met the Dane twice, losing on both occasions, but is relishing the chance to take her on again in Seoul.
"She's a great player - she was number one in the world," Zakopalova told www.wtatennis.com after advancing to the last eight with a 6-1 7-6 (8/6) victory over Slovakia's Magdalena Rybarikova.
"I have to be patient - she doesn't make any mistakes and runs a lot. But I have nothing to lose. I just want to play 100 per cent, just give it my best."
Wozniacki advanced with a 6-2 6-3 win over French qualifier Caroline Garcia.
Sixth seed Varvara Lepchenko beat Anabel Medina Garrigues 6-4 6-1 to reach her fourth quarter-final of the year.
She next meets Tamira Paszek, who won 11 games in a row to dismiss Korean wildcard Lee So-ra 6-2 6-0.
Fourth seed Nadia Petrova was forced out of her match with Maria Jose Martinez Sanchez due to a lower back injury. The Spaniard will play eighth-seeded Ekaterina Makarova next following the Russian's 6-3 7-5 win over American Jamie Hampton.
The final last-eight tie, which was decided on Wednesday, pits third seed Kaia Kanepi against Kiki Bertens.