The second-seeded Beck double-faulted five times in the opening set and saved 12 break points in total. She will play eighth-seeded Karin Knapp of Italy.
Also, 2007 finalist Yvonne Meusburger of Austria defeated third-seeded Irina-Camelia Begu of Romania 6-3, 6-3. Meusburger, who reached the final in Budapast last week, converted seven of 10 break points.
Elina Svitolina of Ukraine beat sixth-seeded Chanelle Scheepers of South Africa 7-5, 1-6, 6-1 and will face Patricia Mayr-Achleitner in the last eight. Svilotina scored just four points against Scheepers' serve in the second set but broke her opponent four times in the decider.
Mayr-Achleitner became the third Austrian player after Meusburger and Lisa-Maria Moser to reach the quarterfinals by defeating Petra Martic of Croatia 6-4, 6-4.