Gremio are still searching for their first win in this season's Copa Libertadores after going down to Universidad Catolica, while Libertad made it three victories from three matches.
Brazilian side Gremio only have one point from three Group H fixtures following Thursday's 1-0 loss away to Catolica – the club's second consecutive defeat in the competition.
After their loss at home to Libertad on matchday two, three-time Libertadores winners Gremio – the 2017 champions – succumbed to Sebastian Saez's 17th-minute goal in Santiago, Chile.
Stefano Magnasco's cross found Argentine forward Saez, who side-footed a volley past Paulo Victor for the Chilean hosts.
Catolica improved to six points, five ahead of third-placed Gremio and three adrift of leaders Libertad.
Paraguayan outfit Libertad preserved their 100 per cent record after accounting for lowly 10-man Rosario Central 2-0.
Second-half goals from Matias Espinoza and Jorge Recalde lifted Libertad as Rosario played out the remaining 15 minutes with 10 men following Marcelo Ortiz's second yellow card.
Meanwhile, Olimpia scored three goals in the second half to blitz hosts Sporting Cristal 3-0 in Group C.