Bellucci broke Haider-Maurer's serve early in the third set and held on to close the match in 2 hours, 36 minutes at the Ibirapuera arena.
Bellucci, ranked 108th, will now play Martin Klizan of Slovakia, who upset third-seeded Marcel Granollers of Spain 6-4, 6-3.
Fourth-seeded Juan Monaco of Argentina reached the quarterfinals with a marathon 7-6 (2), 2-6, 7-5 victory over Albert Ramos of Spain in nearly three hours. He will face Paolo Lorenzi of Italy, who cruised past win Brazilian qualifier Rogerio Dutra Silva 6-4, 6-3.
Top-seeded Tommy Haas will play his quarterfinal match against 116th-ranked Horacio Zeballos of Argentina on Friday.