Miguel Borja scored a second-half brace away from home in Asuncion to put Palmeiras in a strong position on Thursday.
Copa Libertadores holders Gremio suffered a narrow 2-1 loss away to 10-man Estudiantes in the round-of-16 first leg on Tuesday.
Lucas Pratto led River Plate past Santa Fe and into the last 16 of the Copa Libertadores.
Former Benfica striker Oscar Cardozo was the hero, his 90th-minute free-kick preserving Libertad's 100 per cent record in Group Three.
Cicero was the hero for Gremio, coming off the bench to score an 83rd-minute winner against Lanus on Wednesday.
Barcelona won 1-0 on Wednesday but Gremio still progressed to the Copa Libertadores final 3-1 on aggregate.
Brazilian sides Atletico Mineiro and Palmeiras came unstuck against Wilstermann and Barcelona in the last 16 of the Copa Libertadores.
2015 champions River Plate triumphed 2-0 at Paraguayan hosts Guarani in the first knockout round of the Copa Libertadores.
Estudiantes were 3-0 winners at Barcelona but Botafogo's victory saw Juan Sebastian Veron's men eliminated.
Atletico Tucuman beat El Nacional 1-0 to reach the third qualifying phase of the Copa Libertadores - no mean feat given their travel woes.
Atletico Nacional sealed a Copa Libertadores final place thanks to a double from Miguel Borja.
Pumas UNAM head home to Mexico on May 24 with a priceless away goal, after Jose Angulo's brace had put Independiente del Valle in control.
Nacional are into the Copa Libertadores quarter-finals, but defending champions River Plate suffered a last-16 exit.
River Plate clinched their third Copa Libertadores title here Wednesday with a 3-0 victory over Tigres to shatter the Mexican side's dream of winning South America's most prestigious club tournament.