The Brazilians won the first leg by a solitary goal but goals in the 91st and 94th minutes followed an earlier strike from Ignacio Fernandez and were enough to make it 3-1 on aggregate and secure a trophy decided annually between the winners of South America's two premier club competitions.
River's opener came from a VAR-assisted penalty in the 64th minute. Goalkeeper Santos stopped Fernandez's spot kick but the midfielder followed up to open the scoring.
Pratto made it 2-0 with a lovely finish in the dying seconds before Suarez guaranteed the win when he rounded Santos and slotted the ball into the empty net.
It was River's third Recopa following triumphs in 2015 and 2016.
Athletico were in the final after beating Junior of Colombia to win the Sudamericana, the regional equivalent of the Europa League.
River qualified after beating city rivals Boca Juniors to win the Copa Libertadores in a game moved to Madrid because of crowd trouble in Argentina.
(Editing by Greg Stutchbury)
