Barthel needed just over an hour to claim victory at the WTA International hard-court tournament, easing to a 6-4 6-3 win.
The sixth seed moved into the lead as she edged a frenetic first set that featured five breaks of serve.
And Barthel was able to carry that momentum into the second, puncturing the Ukrainian's serve twice more to secure progress into the next round, where she will face the winner of the contest between Monica Niculescu and Magdalena Rybarikova which takes place on Monday.