Looking to equal the record of seven titles held by fellow Argentine side Independiente, Boca went ahead after 15 minutes of the semi-final, first leg at a heaving Bombonera shrouded in riverside mist.
Santiago Silva opened the scoring from close to the penalty spot, taking a cross from fellow striker Pablo Mouche with his back to goal, swivelling and firing low inside the right-hand post.
Left-back Juan Sanchez Mino added the second 10 minutes after half-time to give experienced campaigners Boca a comfortable lead for the second leg in Santiago next Thursday.
Juan Roman Riquelme put Walter Erviti through on the left, goalkeeper Jhonny Herrera parried the midfielder's shot and Sanchez Mino followed through to ram home.
"Next week we'll see if it was good [enough] scoring two goals tonight," Riquelme told Fox Sports TV.
"We played well. In the last 15 minutes, which was when we had most space, maybe we sat back a bit. Perhaps if we'd attacked a bit more we could have hurt them. We're dreaming of playing the final.
"We know that in Chile it's going to be an attractive 90 minutes, they're a good team but we were superior tonight."
The Chilean side, holders of the Copa Sudamericana, found it hard to play their passing game in the Bombonera cauldron and managed few chances, although Boca goalkeeper Agustin Orion had to make a diving save from a free-kick by Marcelo Diaz on the half hour.
The winners of the tie will meet a Brazilian side in the final with Corinthians 1-0 up against holders Santos before the second leg at home in Sao Paulo on Wednesday.
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