The event is called the Nurnberger Gastein Ladies.
Beck rallied to get past Mandy Minella 2-6, 6-4, 6-4 in more than 2 1/4 hours. Beck had five of her six breaks on the day in the last two sets. She won just 53 percent of the points on serve -- a statistic hurt by eight double faults -- but managed to gain a spot in the quarterfinals with three third-set breaks.
Yvonne Meusburger continued her recent strong play with a 6-3, 6-3 win over third-seeded Irina-Camelia Begu with seven breaks in nine games receiving Begu's serve.
Elina Svitolina ousted sixth-seeded Chanelle Scheepers 7-5, 1-6, 6-1, winning nearly 60 percent of the points and finishing off four breaks in the third set.
Also in Thursday's second-round play, Patricia Mayr-Achleitner defeated Petra Martic 6-4, 6-4 and Arantxa Rus, who ended a record 17-match losing streak in the first round, beat Estrella Cabeza Candela 5-7, 7-5, 6-3.
Rus next takes on Meusburger while Beck meets eighth-seeded Karin Knapp in the other quarterfinal in the lower half of the draw. The other matches Friday have Mayr-Achleitner playing Svitolina while Lisa-Maria Moser goes against Andrea Hlavackova.