Gualberto Mojica gave Oriente victory in their first round first leg against Nacional with a scorching strike just after the half-hour.
The side from Santa Cruz in central Bolivia have not qualified for the group stage of South America's premier club competition since 2011.
But a one-goal loss or better next week in Uruguay would see Oriente clinch a spot in a second-round group and dump Nacional from the Copa Libertadores.
Nacional have a strong history in the Copa Libertadores having won the competition three times and reaching the semi-finals as recently as 2009.
On Tuesday in Santa Cruz, the home side scored the only goal of the game in the 33rd minute when midfielder Mojica ran onto Juan Quero's pass in the penalty area and thrashed the ball inside the far post.
In the other first-round first leg, Morelia defeated Santa Fe 2-1 in Mexico, with the Colombian club's late away goal setting up an interesting second clash.
Morelia took advantage of lax marking by their Colombian visitors to score either side of half-time with Hector Mancilla opening the scoring in the 27th minute.
Santa Fe left a huge gap on the left side of their defence and after Armando Zamorano burst into the space to receive the ball, he teed up Mancilla on the overlap.
Zamorano strolled past a couple of defenders to score the Mexican hosts' second goal in the 66th minute but Santa Fe gave themselves hope ahead of next week's second leg when Omar Perez converted a penalty with five minutes remaining.
