After the first leg at Boca's La Bombonera finished scoreless, Leonardo Pisculichi struck the decisive goal after 15 minutes, slotting his shot into the bottom corner of the net to spark celebrations in the Estadio Monumental stands.
It could have been a different story if Emanuel Gigliotti had converted a penalty which was awarded just 20 seconds in, but Marcelo Barovero denied him after Ariel Rojas had upended Cesar Meli.
While River dominated the goal-scoring opportunities against their fellow Buenos Aires-based club, they failed to double their lead but Pisculichi's strike proved to be enough.
Boca had defender Cata Diaz sent off in the final minute when he petulantly kicked Teo Gutierrez, who was attempting to keep the ball at the corner flag.
The victory was River's first in six matches in all competitions, ending a winless run that stretched back to the start of the month.
Pisculichi struck the winner in the 16th minute, sliding a left-foot shot past Agustin Orion's outstretched right hand after a cross from Leonel Vangioni.
River, who have never won South America's second-tier continental competition, will face Atletico Nacional of Colombia in the two-legged final.
Atletico will host the first leg on December 3 before they head to Argentina a week later.
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