The world number 130 broke the Giraldo serve for the fifth time in the match in game eight of the decider and served out for a 3-6 6-4 6-3 triumph over the world number 60 in two hours and 25 minutes.
The two other Brazilians in first-round action on Monday did not fare so well, however, as Argentina's Federico Delbonis and Facundo Bagnis progressed at the expense of Guilherme Clezar and Joao Souza.
Delbonis cruised past wild card Clezar 6-1 6-1, while Bagnis saw off Souza 7-5 2-6 6-2.
Elsewhere in the men's draw, Slovakian qualifier Martin Klizan toppled Spain's Guillermo Garcia-Lopez 6-4 4-6 7-6 (7/4) and Serbian Dusan Lajovic led 6-7 (7/9) 6-3 4-0 against Filippo Volandri when the Italian retired with a right shoulder injury.
In the women's event, third seed Paula Ormaechea of Argentina - South America's highest-ranked player - lost her opening service game but wasted no time thereafter in seeing off American Nicole Gibbs 6-2 6-1.
The only other seed in action on Monday was dumped out, though, as Italian qualifier Nastassja Burnett secured her first main-draw win of 2014 with a 7-5 6-4 success over sixth-seeded Spaniard Maria-Teresa Torro-Flor.
"At the beginning I was playing really well, very aggressive," Burnett said on www.wtatennis.com. "It was a pity at 4-1 that it started to rain and I lost my momentum and she got back in the match.
"It was tougher than I'd like but I'm happy that I got the win and I feel every day I'm playing better."
Also on Monday, Spain's Silvia Soler Espinosa thrashed Brazil's Laura Pigossi 6-0 6-1, Alison Van Uytvanck of Belgium toppled Swede Johanna Larsson 6-4 6-3, Holland's Kiki Bertens was a 7-5 6-0 winner against Montenegrin teenager Danka Kovinic and Pole Katarzyna Piter defeated Brazilian Beatriz Haddad Maia 6-3 6-3.