Almagro won last week in Sao Paulo after capturing both his matches in Spain's first-round Davis Cup triumph over Kazakhstan.
He overwhelmed Federico Delbonis in Thursday's second round 6-3, 6-2 to set up a quarterfinal meeting with qualifier Igor Andreev, who won over seventh-seed Fernando Verdasco 7-6 (7-3), 6-3.
In Thursday's other second-round matches, Carlos Berlocq blasted third-seeded Gilles Simon 6-2, 6-1 and David Nalbandian was a 6-3, 6-1 winner over Juan Monaco. Berlocq and Nalbandian will meet in Friday's quarterfinals.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut