Ferrer, who was the runner-up at this event two years ago, needed just one hour and 17 minutes to take down Bagnis, 6-3, 6-4, on the red clay at Buenos Aires Lawn Tennis Club.
Fourth-seeded Kei Nishikori of Japan came back to beat Romanian's Victor Hanescu 3-6, 7-5, 6-1, while sixth-seeded Swiss Stanislas Wawrinka went the distance to best France's Benoit Paire 6-3, 5-7, 6-2 on Day 3.
Also on Day 3, Fernando Gonzalez of Chile, squeezed past Albert Ramos of Spain, 7-6 (7-6), 7-6 (7-5) in one hour and 50 minutes. Gonzalez will face Ferrer in the quarterfinals while Nishikori and Wawrinka will also square off in the quarterfinals.
In some second-round action on Thursday, second-seeded and defending champion Nicolas Almagro will face Argentine Federico Delbonis in an anticipated all- Argentine affair. The hot Almagro topped Argentine favorite Juan Ignacio Chela in last year's Buenos Aires finale and is fresh off his title in Sao Paulo last week. Monaco was the Buenos Aires winner in 2007 and runner-up in 2009.
The 2012 Buenos Aires champion will earn $82,900.