Striker Santiago Silva headed the winner at the Argentine side's Bombonera cauldron from substitute Pablo Mouche's cross at the end of a second half largely dominated by the Chilean team.
Boca went ahead midway through the first half with a goal from inspirational captain Juan Roman Riquelme that could be a candidate for the best of the competition.
Less than two minutes later, midfielder Walter Erviti almost restored Boca's lead when he darted past three defenders only to see his shot come back off the post.
Espanola had Uruguayan central defender Diego Scotti sent off in added time for chopping Riquelme down and he will miss next Wednesday's second leg in Santiago.
"We did an exceptional job here at La Bombonera, we just lost concentration in the final seconds. We must work hard for the return and be wary because Boca are Boca," Jaime told Fox Sports.
