Boca, six-time Libertadores champion, recorded a 2-0 win over Cruzeiro in the first leg of their quarter-final in Buenos Aires.
Former Lazio, Inter and Fiorentina forward Mauro Zarate opened the scoring nine minutes before half-time, finishing a Pablo Perez pass with the outside of his boot.
Cruzeiro was dealt another blow 15 minutes before full-time, Dede sent off after a heavy collision with Boca goalkeeper Esteban Andrada, with the video assistant referee (VAR) needed.
The host team made the most of its numerical advantage with eight minutes remaining, Perez producing a fine strike from the edge of the area.
The result has left Cruzeiro with work to do heading into the second leg on 4 October.
In the all-Argentinian tie, Independiente was held to a 0-0 draw at home to River in the first leg of their quarter-final.