Bellucci, a native of Tiete, Brazil, dropped the first set but rebounded to log a 3-6, 6-4, 6-3 victory over Giraldo at Jockey Club Brasileiro.
He was joined the second round by Argentina's Federico Delbonis, who advanced with a 6-1, 6-1 pasting of Brazilian Guilherme Clezar.
Other Day 1 winners included Serbia's Dusan Lajovic, who bested Filippo Volandri of Italy 6-7 (7-9), 6-3, 4-0, retired, and Slovak Martin Klizan, who outlasted Spaniard Guillermo Garcia-Lopez 6-4, 4-6, 7-6 (7-4).
Facundo Bagnis of Argentina also notched a victory, getting past Brazilian Joao Souza 7-5, 2-6, 6-2.
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