The second-seeded Almagro, who has been piling up victories on the clay court swing this winter, advanced by downing Benoit Paire 3-6, 6-3, 6-4.
Almagro won the championship two weeks ago in Sao Paulo and lost a three-set finals match last week in Buenos Aires to David Ferrer, who is seeded No. 1 in this event.
Ferrer also moved on Wednesday with a 6-3, 6-3 decision over Lukasz Kubot.
Almagro will take on Fernando Verdasco in the quarterfinals after Verdasco disposed of Juan Ignacio Chela 6-4, 6-2. Ferrer's quarterfinal opponent will be Pablo Andujar, who rallied to down Florian Mayer 4-6, 7-5, 6-4.
In the rest of the second-round matches, Carlos Berlocq defeated Potito Starace 6-1, 6-4, Santiago Giraldo ousted Marcel Granollers 6-4, 6-4, Stanislas Wawrinka survived against Albert Ramos 6-3, 3-6, 6-3 and Jeremy Chardy came back to defeat Kei Nishikori 1-6, 7-6 (10-8), 6-0.
Ferrer, Almagro and the No. 8 Verdasco are the only seeded players to reach the quarterfinals.