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.
Beyonce flaunts bikini body, Blue Ivy in vacation pics
Couple mistakenly served bag of cash at McDonald's drive-thru