Ignacio Fernandez and Rafael Borre both scored penalties in each half to lead River past Paraguayan visitor Cerro Porteno in Buenos Aires.
River – seeking back-to-back Libertadores titles after upstaging bitter rival Boca Juniors in last year's final – took the lead thanks to a VAR review in the eighth minute.
After reviewing a handball against Joaquin Larrivey in the penalty area, Fernandez eventually stepped up to convert the spot-kick despite Cerro Porteno protests.
River forward Borre made it 2-0 for the Argentine giant with a penalty of his own in the 65th minute.
After having a goal ruled out 12 minutes earlier in the wake of a foul in the build-up, Borre made no mistake from the spot.
River will travel to Cerro Porteno for the return leg on 29 August, with a potential semi-final against Boca awaiting the Libertadores holder.