Fognini appeared on the verge of an upset in Buenos Aires after moving into a 3-2 lead in the decisive third set courtesy of a break.
But top seed Nalbandian broke the Italian in the sixth game to pull level before reeling off the final three games to set-up a last eight meeting with Potito Starace, who posted a 6-3 6-3 victory against Juan Pablo Brzezicki.
Poor serving contributed to the struggles of Nalbandian, who had four aces and six double-faults in the two-hour 32-minute contest.
Starace is participating in his second tournament since serving a six-week ATP-imposed suspension for betting on matches.
Fifth seed Nicolas Almagro, fresh from winning his third career title on Sunday at Costa Do Sauipe, booked a quarter-final berth courtesy of a 6-2 2-6 6-3 win over fellow Spaniard Oscar Hernandez.
Almagro will next face Juan Ignacio Chela, who moved into the quarter-final with a 6-4 6-4 victory over Brazilian qualifier Thomaz Bellucci.