Banfield, who have taken a maximum six points in Group Six, went in front in the 36th minute of the match in Cuenca, 2,850 metres above sea level, with a shot from outside the box by midfielder Walter Erviti.
Uruguay striker Sebastian Fernandez added another two minutes later from a rebound after goalkeeper Esteban Dreer had parried Ruben Ramirez's header.
Fernandez made it 3-0 with a header on the hour and Colombian James Rodriguez made it 4-0 11 minutes later.
The Argentine side had defender Marcelo Bustamante sent off for a second yellow card offence six minutes from time and in the 86th midfielder Gabriel Mendez pulled a goal back with a penalty.
Banfield's progress was not matched by Lanus, their arch-rivals from the southern suburbs of Buenos Aires, who lost their second Group Four match in succession, 2-0 away to Universitario in Lima.
The Peruvian side, who scored through Piero Alva and Gianfranco Labarthe, are joint top of their group with Paraguay's Libertad on a maximum six points.
Libertad crushed nine-man Blooming of Bolivia 4-0 in Asuncion on Tuesday with two goals from striker Rodolfo Gamarra.
South American champions Estudiantes of Argentina are away to Peru's Alianza Lima in Group Three on Thursday.
