Almagro led four Spaniards into the last eight, including second-seeded Tommy Robredo.
Top-seeded Almagro lost his serve twice but improved to 4-0 against Vassallo Arguello.
"I played better (than in the first round), but I still have to improve a lot,'' Almagro said. "I'm not at the level I was in 2008.''
In the quarterfinals he'll meet Frederico Gil of Portugal, who upset fifth-seeded Marcel Granollers of Spain 7-5, 3-6, 6-3.
Robredo eased past Fabio Fognini of Italy 6-2, 6-2 to set up a quarterfinal with countryman Alberto Martin, who ousted seventh-seeded Nicolas Devilder of France 6-2, 7-6 (4).
Spain's Juan Carlos Ferrero - the world's top-ranked player in 2003 but now 101st - continued his nice run by breezing past Brian Dabul of Argentina 6-1, 6-2. Ferrero's 11th and last title was in 2003.
Fourth-seeded Jose Acasuso of Argentina, runner-up in Chile last week, defeated Pablo Cuevas of Uruguay 6-3, 6-2 and will meet compatriot and sixth seed Eduardo Schwank, who earned a 2-6, 7-6 (4), 7-6 (6) win over Portuguese qualifier Rui Machado.
Thomaz Bellucci beat Polish qualifier Lukasz Kubot 5-7, 6-4, 6-4 to be the only Brazilian to reach the quarterfinals - his first at home - where he'll meet Ferrero.
Capello Satisfied With Spain Test
Almagro gets through first round in Brazil Open
