Bellucci broke Giraldo's serve to go up 4-2 in the final set, then held on to close out the match in just over two hours at the Ibirapuera arena. The break came right after Giraldo called for treatment on his lower back in between games.
The 108th-ranked Bellucci, playing on a wild card, had six aces, including three in the decisive set.
"I couldn't hold on to a 3-0 lead in the first set but I started playing better after that," Bellucci said. "It makes a big difference to be playing at home with the support of the fans. They got behind me and I got to play more aggressively toward the end. It made a huge difference."
Bellucci beat Giraldo in three sets last week at the Rio Open. The 26-year-old Brazilian will face Andreas Haider-Maurer of Austria in the second round.
Earlier Tuesday, Brazilian qualifier Rogerio Dutra Silva defeated sixth-seeded Guillermo Garcia-Lopez of Spain 1-6, 7-5, 6-3 in 2 hours, 17 minutes. Albert Montanes of Spain beat Aljaz Bedene of Slovenia 6-2, 6-2, while Federico Delbonis of Argentina defeated Filippo Volandri of Italy 6-1, 6-2.
Defending champion Rafael Nadal is not playing at the clay-court tournament this year. He won the Rio Open last week.
Top-seeded Tommy Haas of Germany, ranked 12th, will open against qualifier Potito Starace of Italy on Wednesday. Second-seeded Nicolas Almagro of Spain will play Delbonis, while third-seeded Marcel Granollers plays Martin Klizan of Slovakia.