Rybarikova, 23, had little trouble dispatching the South African, reeling off a 6-2, 6-1 victory on the hard courts at the William H.G. FitzGerald Tennis Center.
Scheepers wasn't the only seeded player to fall Monday -- No. 5 Barbora Zahlavova Strycova of the Czech Republic took a tumble at the hands of Hungarian Edina Gallovits-Hall 7-5, 4-6, 6-3.
Third-seeded American Sloane Stephens beat Sesil Karatantcheva of Kazakhstan 6-3, 2-6, 6-1.
Other Day 2 winners included seventh-seeded American Coco Vandeweghe, eighth-seeded Belarusian Olga Govortsova, Swede Johanna Larsson, Slovak Jana Cepelova, Greek Eleni Daniilidou, Hungarian Melinda Czink, American Irina Falconi and France's Aravane Rezai.