South Africa's Scheepers dropped the first set against Venezuelan qualifier Adriana Perez but then bounced back to post a 2-6, 6-4, 6-0 victory before rain washed out four matches which were postponed or suspended.
Kazakhstan's Shvedova, however, didn't fare as well, falling to Hungarian Melinda Czink 6-2, 4-6, 2-6 in another first-round matchup.
Also logging victories Monday were Romania's Monica Niculescu, who got past sixth-seeded Anabel Medina Garrigues of Spain 5-7, 7-6 (9-7), 6-1, and Spanish qualifier Beatriz Garcia Vidagany, who dispatched Russia's Nina Bratchikova 6-4, 6-2.
Frenchwoman Caroline Garcia and Croatian qualifier Tereza Mrdeza also posted first-round wins.
A scheduled match featuring top-seeded American Venus Williams was among those postponed Monday.