Czink's 4-6, 6-3, 7-5 win was her first in WTA singles competition.
"It feels great. I haven't really processed it yet but I will," Czink said. "I went match-by-match this week. This was the toughest match this week ... We really pushed each other, and I'm happy I could come out the winner."
Safarova was trying to win for the fifth time on the tour.
"We both played a good match," Safarova said. "I think it just came down to a few balls and she did it better."