Nacional went ahead one minute before halftime in Montevideo when Alexander Medina laid the ball into the path of Alvaro Fernandez, who fired into the roof of the net from close range.
Their second goal was a bizarre effort which came as River threatened an equaliser.
Marcos Mondaini's shot was parried onto the post by River goalkeeper Mariano Barbosa but the ball then hit Barbosa and bounced into the net.
Mauricio Victorino added the third with the last kick of the game when he floated in a free kick in the fifth minute of injury-time.
Nacional, who top Group Three with nine points from three games, had Santiago Garcia sent off for kicking an opponent in injury-time.
Twice former champions River are third with three points in as many games.
Earlier, Mauro Boselli scored a hat-trick to give River's fellow Argentines Estudiantes a 4-0 win over Ecuadorean champions Deportivo Quito in Group Five.
Boselli headed his first in the fourth minute and latched onto Leandro Benitez's pass to score the second in the 25th.
Enzo Perez added the third one minute before halftime when he slotted the ball past Bonard Garcia after the Deportivo defence was caught out by a long goal kick from Mariano Andujar.
Boselli completed the scoring with another header in the 69th minute to leave Estudiantes with six points from four games, four behind leaders Cruzeiro.
