Spain's Dominguez Lino -- a two-time titlist in Bogota -- moved on with a 3-6, 6-2, 6-1 victory over Colombian wild card Catalina Castano while Schiavone, a former French Open winner, bested Canadian qualifier Sharon Fichman 4-6, 6-4, 6-4.
Also advancing Tuesday was fifth-seeded Flavia Pennetta of Italy, who got past 2012 finalist Alexandra Panova of Russia 4-6, 6-3, 6-3.
Two other seeds fell, however, in Tuesday's opening-round action.
Sixth-seeded Dutchwoman Arantxa Rus was upended 6-4, 6-3 by Spaniard Maria-Teresa Torro-Flor, while No. 7 Pauline Parmentier of France fell to Croatian qualifier Tereza Mrdeza 7-6 (7-5), 6-4.
Also logging wins were eighth seed Timea Babos of Hungary, defending champion Lara Arruabarrena-Vecino of Spain, Romanian Alexandra Cadantu, Brazilian qualifier Teliana Pereira and Italian Karin Knapp.
Celebrity Families of 2014 [PHOTOS]