Matias Suarez and Esequiel Barco scored in the final 10 minutes for the four-time Libertadores winners in an overall cagey 90 minutes at the Monumental David Arellano.
Los Albos had an apparent penalty waved away in first-half injury time, when Paulo Diaz brought down Juan Lucero as he was cutting back onto his right foot to shoot.
Diaz would be prominent again with Matias Suarez breaking the deadlock for River in the 83rd minute, though. The Chile international and former Colo Colo player quickly won back possession before playing through Marcelo Herrera, whose cross was not dealt with, and Suarez was on hand to punish.
Returning from injury, Esequiel Barco played a full match and doubled the margin in the 88th minute, rifling home from just outside the penalty area, before Lucero scored a consolation in the second minute of injury time.
Palmeiras took control of Group A and secured its third win of this season's group stage, with the 2021 Libertadores winner defeating Emelec 3-1 in Guayaquil.
The Verdao have not struggled for goals despite a middling start to the Serie A season, and they opened the scoring in spectacular fashion in the 19th minute.
Following Mayke's cross-field pass, Rony headed in Wesley's first-time delivery back across the penalty area, with the ball not touching the ground in that sequence.
Gabriel Veron made it 2-0 six minutes later, cutting through the Emelec defence in transition, before calmly slotting home past Pedro Ortiz. Joao Rojas scored for the hosts in the 61st, but Breno Lopes eventually restored the two-goal margin.
In the other Group F result, Fortaleza claimed its first-ever win in the Libertadores, defeating Alianza Lima 2-1 at home on Thursday (AEST).
After two respective defeats to begin their Serie A and Libertadores campaigns, Silvio Romero put Fortaleza ahead five minutes after the restart.
Alianza claimed an equaliser in the 70th minute with Pablo Lavandeira getting on the end of Yordi Vilchez's cross, but Yago Pikachu got his second assist of the night, setting Hercules up for the winner nine minutes later.