Almagro, who won the Brazil Open on Saturday for his eighth ATP title, rallied to defeat Mayer 6-7 (3), 6-1, 6-3. All of his titles have come on clay -- the surface in Buenos Aires.
Almagro converted five of eight break points and had nine aces compared to Mayer's two. Almagro has won 11 of 13 matches this season and has reached the quarterfinals -- or better -- three times in this tournament.
In other second-round matches, third-seeded David Nalbandian of Argentina defeated countryman Juan Pablo Brzezicki 6-1, 6-2. He will face Spain's Tommy Robredo in Friday's quarterfinal. No. 6 Robredo defeated Albert Ramos-Vinolas of Spain 6-3, 7-5.
"Obviously he [Nalbandian] is the favorite and he has a lot of fans in this country," Robredo said. "When he plays well he is almost unstoppable."
Robredo won the Movistar Open earlier this month in Chile, another clay-court event.