Hradecka took out seventh-seeded Tamira Paszek of Austria 6-3, 7-6 (10-8) and Rybarikova outlasted Spain's Suarez Navarro, the No. 8 seed, 7-6 (7-2), 6-4 in the opening round.
Ninth-seeded Mona Barthel of Germany eliminated Luxembourg wild card Mandy Minella 7-5, 6-0.
Romanian Monica Niculescu, last year's Luxembourg runner-up, battled to a 7-6 (7-4), 6-1 triumph over Romina Oprandi of Switzerland.
Belarusian Victoria Azarenka, the defending champion, is not entered in this year's event.
Celebrity Families of 2014 [PHOTOS]