River were beaten 2-1 by Peruvian champions Deportivo San Martin while San Lorenzo lost 2-0 to Paraguayan champions Libertad.
Brazilian champions Sao Paulo beat their Colombian counterparts America 3-1 away in the other match.
Argentine sides have lost five out of six away matches between them so far in this year's competition.
Boca Juniors broke the sequence on Wednesday when they beat Venezuela champions Deportivo Tachira 1-0 in San Cristobal.
River, playing their first away game, fell behind to a Jose Diaz penalty in Lima before Gonzalo Ludena added a second with a long-range shot for the Peruvians after halftime (pictured).
Radamel Falcao Garcia pulled one back for Nestor Gorosito's team in the 68th minute of the Group Three match.
Both teams have three points from two games in the group, which is led by Uruguay's Nacional who have six.
San Lorenzo, beaten 1-0 in Peru by Universitario two weeks ago, suffered an early injury to goalkeeper Agustin Orion against Libertad and his replacement Bruno Centeno was at fault for the first goal in the 25th minute.
Centeno failed to hold Sergio Aquino's shot and Miguel Ximenes pounced to open the score. Six minutes later, Aquino added another with a long-range effort.
Libertad, Paraguayan champions four times in a row, top Group Eight with nine points from three games. San Lorenzo and Universitario have three each.
Striker Washington, whose goals last year helped Fluminense reach the final, scored twice in the first half hour to set Sao Paulo on their way to a comfortable win in Colombia against America.
Borges added another four minutes after the restart to send the Brazilians top of Group Four with four points, ahead of Uruguay's Defensor Sporting on goal difference.
America, who replied with late Victor Cortes goal, have lost their first two games.
