The second-seeded Beck double-faulted five times in the opening set and saved 12 break points in total. She will next 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 will next play Arantxa Rus of the Netherlands, who rallied from a set and a break down to beat Estrella Cabeza Candela of Spain 5-7, 7-5, 6-3.
Results from the fourth day of the WTA Bad Gastein Open on Thursday (x denotes seeding):
Patricia Mayr (AUT) bt Petra Martic (CRO) 6-4, 6-4
Elina Svitolina (UKR) bt Chanelle Scheepers (RSA x6) 7-5, 1-6, 6-1
Arantxa Rus (NED) bt Estrella Cabeza (ESP) 5-7, 7-5, 6-3
Yvonne Meusburger (AUT) bt Irina Begu (ROM x3) 6-3, 6-3
Annika Beck (GER x2) bt Mandy Minella (LUX) 2-6, 6-4, 6-4