The Brazilian outfit produced an emphatic display in the first leg of the semi-final in Argentina.
Rony opened the scoring and Luiz Adriano doubled the lead early in the second half, with Matias Vina sealing the win after Jorge Carrascal was sent off for River.
River, finalist in the previous two editions of the Libertadores, fell behind in the 27th minute after a huge error.
Franco Armani dealt poorly with a cross, his clearance with his feet falling to Rony, whose volley beat the River goalkeeper via a slight deflection.
Palmeiras – which had another effort ruled out for offside in the first half – doubled the lead shortly after the break.
Luiz Adriano easily turned Robert Rojas after a pass from Danilo before producing a fine composed finish past Armani.
Making matters worse for River, Carrascal was sent off for a rash challenge on Gabriel Menino on the hour-mark.
The host side was punished almost immediately, Vina heading in a Gustavo Scarpa set-piece to make it 3-0.
Palmeiras went close to adding a fourth late on, but River has a huge mountain to climb in the second leg in Sao Paulo on 12 January.