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.
Charlize Theron not engaged to Sean Penn 'yet'
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend