Juan Carlos Arce's 87th-minute goal saw Bolivar edge Argentina's Lanus 1-0 at home, completing a 2-1 aggregate victory.
The Bolivians will face another Argentine team in the last four, with a tie against San Lorenzo awaiting them in July.
Trailing to an away goal, Lanus' task was made tougher when defender Carlos Izquierdoz was shown a straight red card just before the hour-mark.
Arce scrambled in the only goal of the second leg with three minutes remaining.
In a one-on-one, Bolivar attacker Gerardo Yecerotte chipped an effort against the post, but his team-mate was quickest to react to tap into an open goal.
The last-four tie equals Bolivar's best ever appearance at a Copa Libertadores, having also reached the semis in 1986.
Uruguayan outfit Defensor Sporting was far more comfortable in progressing, claiming a 1-0 win at home to Colombia's Atletico Nacional to complete a 3-0 aggregate victory.
Nicolas Olivera, who also scored in the first leg, struck in the 90th minute to seal the win and his side face Paraguayan side Nacional in the last four.
As the visitors poured numbers forward in search of a much-needed goal, Defensor Sporting hit on the counter-attack.
Leonardo Pais was released down the right and his cross found substitute Olivera to tap in the easiest of goals.
