Boca edged the second leg 1-0 but it was not enough as defending champion River prevailed 2-1 on aggregate in the Superclasico.
River takes out the first leg 2-0:
Jan Hurtado gave Boca hope with his 80th-minute goal, but the host was unable to find a second goal to force penalties at La Bombonera.
River carried a 2-0 lead into the return leg of a rematch of the 2018 all-Argentinian Libertadores final, which had to be rearranged and moved to Real Madrid's Santiago Bernabeu in December after the match was twice suspended in November due to an attack on Boca's team bus by supporters.
Kick-off in Buenos Aires was delayed by 15 minutes due to excess confetti on the pitch as leaf blowers were brought out to clear the field.
When play finally got underway, Carlos Tevez's Boca found the back of the net in the 22nd minute but it was ruled out for handball.
A stunning goal-line block to deny River approaching half-time threatened Boca, though another offside call eased the pressure on the home side.
Enzo Perez almost turned the ball into his own net moments later, however, River goalkeeper Franco Armani produced a fine reflex save to prevent embarrassment.
With time running out, Boca refused to surrender and gave themselves hope when Hurtado found the back of the net following a set-piece 10 minutes from the end.
Another free-kick almost saw Boca level with two minutes remaining, however, River were not to be denied bragging rights as Flamengo or Gremio await in the final.