Both players returned well, with Beck breaking Cepelova's serve five times and the Slovakian breaking Beck's serve on three occasions.
Beck's win sets up a quarterfinal with Bojana Jovanovski, who beat Aleksandra Krunic 6-4, 6-3 in an all-Serbian second-round match. Jovanovski won her only previous meeting with Beck 7-5, 6-3 in Hobart last year.
Second-seeded Carina Witthoeft of Germany is out after she was beaten 4-6, 6-2, 6-2 by Croatia's Donna Vekic, whose reward is a quarterfinal against another German, Anna-Lena Friedsam.
Fifth-seeded Katerina Siniakova of the Czech Republic lost 7-6 (4), 6-3 to Ukrainian qualifier Kateryna Kozlova, while sixth-seeded Margarita Gasparyan of Russia was beaten 6-3, 6-4 by Friedsam.
Besides Beck, the only other seeded player left in the draw is Sweden's Johanna Larsson, the fourth seed. She cruised past Uzbekistani wildcard Nigina Abduraimova 6-2, 6-2.
Larsson's quarterfinal opponent is Russian Evgenia Rodina, who beat Kazakhstan's Yaroslava Shvedova 6-4, 7-6 (4).