There was all to play for heading into the second leg in Montevideo following a goalless first encounter.
Cobreloa enjoyed the better of the early exchanges and opened the scoring in the 11th minute courtesy of a fierce cross-shot from midfielder Hugo Droguett.
Jorge Diaz's team doubled their advantage eight minutes later when Gaston Lezcano finished off a swift counter-attack.
Cobreloa goalkeeper Sebastian Contreras was dismissed 11 minutes before half-time for chopping down home forward Carlos Nunez outside the box.
Nunez and visiting defender Diego Silva also saw red 12 minutes into the second period after an unsavoury altercation.
There were no further goals, though, meaning the Calama-based outfit advanced 2-0 on aggregate and will face Colombian club La Equidad in the second stage.
Elsewhere, Paraguayan side Libertad drew 0-0 at home to Montevideo Wanderers but advanced thanks to last week's 2-1 first-leg win in Uruguay.
Libertad will tackle Mineros in the second stage after the Venezuelan team defeated Ecuadorian giants Barcelona 2-0 at Monumental Stadium for a 4-2 aggregate success, Richard Blanco doing the damage with a fine first-half brace.
Paraguayan side Guarani hammered Oriente Petrolero 4-1 in Bolivia, winning by the same score on aggregate, to secure a meeting with Colombian outfit Nacional.
Federico Santander set the visitors on their way with a first-half double and, although Pablo De Muner gave Petrolero hope by halving their deficit nine minutes into the second half, further away goals from Derlis Gonzalez and Jorge Benitez put the result beyond doubt.
Ecuadorian team Independiente also triumphed away from home to clinch their progression in the tournament, prevailing 2-0 on the night and overall against Venezuelan side Deportivo.
Fernando Guerrero broke the deadlock via a 20th-minute penalty after Jose Granados had fouled playmaker Junior Sornoza, and added his and his team's second midway through the second half on the counter-attack to set up a second-stage clash with Universidad de Chile.