Ismael Blanco's 15th-minute goal was all the Ecuadorians needed to claim a key win at their Estadio Monumental Isidro Romero Carbo.
Libertad will still fancy their chances of progressing when they host the return leg in Paraguay on Wednesday.
The game's only goal came on the back of a fine team move.
Matias Oyola was eventually freed down the left before he squared a pass for Blanco to power high into the net in a one-on-one.
It leaves Barcelona well-placed to reach the round of 16, but they will need a positive result away from home.
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