River advanced to the quarters despite Wednesday's (AEST) 1-1 second-leg draw at home to Guarani, while Lanus went through to the last eight thanks to its 1-0 victory over The Strongest.
Champion in 2015, River progressed 3-1 on aggregate after Lucas Alario cancelled out Marcelo Palau's first-half opener in Buenos Aires.
River was 2-0 the winner against the Paraguayan host last month, but Guarani managed to reduce the deficit at Estadio Monumental Antonio Vespucio.
Guarani kept the tie alive when Palau headed home from an acute angle in the second minute of first-half stoppage-time.
River restored its two-goal cushion seven minutes into the second half as Alario bundled the ball over the line.
Lanus claimed a 2-1 aggregate victory thanks to Jose Sand's 85th-minute winner against visiting The Strongest.
With the last-16 clash deadlocked at 1-1, Sand sent Lanus into the next round after being played through by Nicolas Pasquini for a simple finish.