First-half goals to Andres D'Alessandro, Ignacio Fernandez, Camilo Mayada, Emanuel Mammana and Lucas Alario all but secured victory for the hosts before halftime on Wednesday, reports Xinhua.
Fernandez added a sixth goal seven minutes from time as River overtook their Bolivian rivals at the top of Group 1.
The Argentine outfit now have eight points from four matches, a point ahead of The Strongest with third-placed Sao Paulo two points further back.
In other matches on Wednesday, Palmeiras drew 3-3 at Rosario Central, Independiente del Valle beat Atletico Mineiro 3-2 and Corinthians drew 1-1 at Independiente Santa Fe.(IANS)