Argentina's Ormaechea breezed past American qualifier Nicole Gibbs 6-2, 6-1 in a 62-minute match at Jockey Club Brasileiro.
Spain's Torro-Flor, however, tumbled to Italian Nastassja Burnett 5-7, 4-6.
Other opening-round winners included Belgian Alison Van Uytvanck, Dutchwoman Kiki Bertens, Spaniard Silvia Soler-Espinosa and Poland's Katarzyna Piter.
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