The world number one had won the first set 7-5, but her Australian opponent was forced to concede at 2-2 in the second.
Swiatek is now the female player with the most wins in a single year (58) in the last five seasons. Former world number one Ash Barty recorded 57 victories in 2019.
The second seed in Ostrava is out after Paula Badosa was beaten 7-6 (7-4) 6-4 by Petra Kvitova in front of a delighted Czech crowd, while Elena Rybakina is also through to the last eight after coming from behind to win against Aliaksandra Sasnovich 6-7 (5-7) 6-4 7-5.
The day's two other matches saw more success for Czech participants as Karolina Muchova beat seventh seed Beatriz Haddad Maia 6-4 6-4, while Barbora Krejcikova defeated Shelby Rogers 6-2 6-2.
There was less Czech joy at the Jasmin Open in Tunisia, where Katerina Siniakova was beaten 7-5 6-2 by Claire Liu.
Elsewhere, number three seed Alize Cornet eased past Harriet Dart 6-3 6-4, Elise Mertens came from behind to beat Despina Papamichail and Diane Parry went through against French compatriot Lucrezia Stefanini after the latter retired hurt in the second set.