Mauro Matos and Emmanuel Mas set up the first-leg win with first-half headers at their Estadio Pedro Bidegain home.
Juan Ignacio Mercier and Julio Buffarini added goals in the second half to go with another from Mas to see the Argentine side take control of the semi-final tie.
Bolivar will be left rueing their poor marking from set-pieces as they left themselves with close to no chance of advancing heading into the return leg on July 30.
Edgardo Bauza's hosts needed just six minutes to capitalise on the Bolivians' poor marking and organisation.
There was a hint of offside as Leandro Romagnoli delivered a set-piece but Matos took his opportunity, heading in after Bolivar goalkeeper Romel Quinonez was left stranded having come to try and punch.
Bolivar failed to learn from their mistakes and conceded again in the 28th minute.
Romagnoli's free-kick from the right was well weighted and Mas, in plenty of space in the area, headed in to make it 2-0.
Mercier added a third in the 70th minute with a neat finish before Buffarini, and Mas again, all-but sealed San Lorenzo's place in the final.
Buffarini's goal was a stunner, taking a touch before firing a powerful 30-yard effort past Quinonez, and Mas completed the scoring soon after.