Trailing to a Santiago Garcia brace, Palmeiras rallied to secure a 2-2 draw in Mendoza.
Garcia headed in the opener from close range in the sixth minute before doubling the lead just before the half-hour mark.
However, Felipe Melo brought Palmeiras back into the encounter with a 34th-minute header.
Incredibly, Garcia had a chance to complete his hat-trick before half-time, but the forward had a penalty saved by Palmeiras goalkeeper Weverton.
The hosts were punished for that miss just before the hour-mark, Miguel Borja taking a Luan pass before a brilliant turn and finish, putting the Brazilians in a decent position ahead of next week's second leg.
River Plate, defending their title, could be left to rue a late penalty miss after drawing 0-0 at home to Cruzeiro.
Awarded a spot-kick following a VAR review, River – who had the better of the chances throughout – saw Matias Suarez blaze the 99th-minute penalty over the crossbar.
In the day's other game, LDU Quito took a step towards the quarter-finals with a 3-1 win at home to Olimpia.