Almagro handled Argentine Federico Delbonis 6-3, 6-2 in 73 minutes on the red clay at Buenos Aires Lawn Tennis Club.
Argentine crowd favorite Carlos Berlocq blew away the French Simon 6-2, 6-1 in 66 minutes.
The former Wimbledon runner-up Nalbandian titled here in 2008, while Monaco was the Buenos Aires winner in 2007 and runner-up in 2009.
Meanwhile, qualifier Igor Andreev posted an upset by dousing seventh-seeded Spaniard Fernando Verdasco 7-6 (7-3), 6-3. The tight match featured only three breaks of serve, including two for the winner from Russia.
Andreev will do battle with Almagro in the quarters.
The 2012 Buenos Aires champion will earn $82,900.