Nacional, of Paraguay, had a home 1-0 win over Venezuela side Zamora in Group 4.
Julian Benitez's shot was saved by Zamora goalkeeper Alexis Angulo, but Marcos Melgarejo was on hand to tap into the empty net in the 10th minute.
It was all Nacional needed to earn all three points, as they eyeballed Santa Fe and Atletico Mineiro, although the latter pair are yet to play their second match.
Bolivia club The Strongest also had a 1-0 win, beating Peru side Universitario in La Paz.
Diego Wayar scored in the 71st minute to give The Strongest their first points in Group 1 - seeing them level Atletico PR and Velez Sarsfield.
Atletico PR and Velez Sarsfield are still to play in matchday two.
Wayar's strike, lashed home from outside the area, broke the deadlock, and was the midfielder's first goal for the club since April 2012.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
