Almagro took the first set easily, but thereafter found the going tough as the Argentinean started stretching him on every point and lost the next two sets.
Top-seeded Tommy Haas beat qualifier Potito Starace 7-6 (2), 6-3 to reach the quarterfinals, reports Xinhua.
The 12th-ranked Haas served well throughout the match at the Ibirapuera arena, allowing only one break point to the Italian.
Both players held serve until the first-set tiebreak, when Haas stepped up his game to easily clinch the set.
The German then broke Starace’s serve twice in a row late in the second set to close out the match in one hour, 30 minutes.
Hass will next play Argentina’s Horacio Zeballos, who defeated countryman Guido Pella 6-3, 6-4.
1-Tommy Haas (Ger) beat Potito Starace (Italy) 7-6 (2), 6-3; Federico Delbonis (Arg) beat 2-Nicolas Almagro (Esp), 3-6, 6-3, 6-2; Albert Montanes (Esp) beat Joao Souza (Brazil) 6-4, 2-3, retired; Horacio Zeballos (Arg) beat Guido Pella (Arg) 6-3, 6-4; 3-Klara Zakopalova (Cze) beat Alize Lim (Fra) 6-3, 6-3; 5-Monica Niculescu (Rom) beat Danka Kovinic (Mont) 6-3, 6-1; Alison Van Uytvanck (Belg) beat 8-Paula Ormaechea (Arg) 6-2, 6-2; Alexandra Dulgheru (Rom) beat Teliana Pereira (Brazil) 7-5, 6-2.