It also marked River's first defeat under coach Eduardo Coudet, leaving them second in Group B of the Apertura standings on 26 points, while Boca Juniors climbed to third in Group A with 24.
In a tight first half, captain Paredes made no mistake from the spot just before the break to silence a fervent Estadio Monumental, after the VAR ruled Lautaro Rivero had handled in the box.
The hosts had looked the better side in the opening exchanges but were dealt an early blow when striker Sebastian Driussi went off injured.
Boca went close to doubling their lead after the restart when Santiago Ascacibar drew a fine save from goalkeeper Santiago Beltran, before the visitors took their foot off the gas.
A spirited River pushed for an equaliser but offered little in the way of clear-cut chances, while Boca threatened on the counter, with Beltran making a couple of key saves to keep the deficit to one.
River’s late push ended in frustration as their stoppage-time penalty appeals were waved away, with no VAR intervention.