First-half goals from Diego Gonzalez and Santiago Silva put Lanus in control in Buenos Aires before Victor Ayala added a third in the 72nd minute.
After playing out a 0-0 draw in the first leg, Lanus' progression was never in doubt from that point and Teofilo Gutierrez netted a late consolation for the hosts.
Lanus only needed seven minutes to go ahead at the Estadio Monumental Antonio Vespucio Liberti as Gonzalez diverted in Leandro Somoza's drive from the edge of the area.
Silva tapped in a simple goal on 32 minutes as Lanus took control of the tie against their fellow Argentina Primera Division side.
Lucas Melano's cross from the right was cleverly dummied and Silva was on hand at the back post to tap into an open net.
More terrible defending led to Lanus' third as Lautaro Ayala's pass found unmarked substitute Ayala to side-foot home.
Gutierrez's close-range header meant little as Lanus easily progressed to the last four.
In Colombia, Sao Paulo held on for a 0-0 draw against Atletico Nacional to reach the semi-finals with a 3-2 aggregate win.
Antonio Carlos' late winner in the first leg proved to be vitally important for the defending champions.
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