Godoy Cruz played the last 10 minutes with nine men and Diego Maradona's Gimnasia y Esgrima La Plata punished them.
Franco Armani was the hero as River Plate edged Cruzeiro in the last 16 of the Copa Libertadores.
Palmeiras salvaged a 2-2 draw at Godoy Cruz in an entertaining first leg of their Copa Libertadores last-16 tie.
The draw for the Copa Libertadores round of 16 took place in Paraguay on Monday.
The pots are set for the last 16, with the draw scheduled to take place in Paraguay on Monday.
Cruzeiro made it five wins from five games in Group B as Atletico Mineiro failed to progress.
Paolo Guerrero hits a double to sink Palestino 3-2 as Brazilian side Internacional seal their place in the last 16 of the Copa Libertadores.
Nicolas De La Cruz's spectacular free-kick helped River Plate earn a draw at Internacional in the Copa Libertadores.
Boca Juniors and Palmeiras both won 3-0 in the Copa Libertadores on Tuesday.
Last season's runners-up Boca Juniors were held by Bolivian hosts Jorge Wilstermann in Group G on Tuesday.