River won the first leg of the semi-final 2-0 at their home stadium earlier this month and were on the back foot for large parts of the match but it was not until the last few minutes that Boca threatened River's two-goal lead.
Substitute Jan Hurtado got on the end of Lisandro Lopez's commanding header with just 10 minutes left but the home side could not get the all-important equaliser.
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The match, which came less than a year after violence interrupted the competition final between the same two clubs, was delayed for 15 minutes due to the amount of ticker tape on the pitch but passed without any major security incidents.
Last year the second leg of the final was moved to Spain after River fans attacked the Boca coach as it neared River Plate's Monumental stadium.
And in 2015 Boca were kicked out of the competition after their fans attacked the River players with pepper spray in the tunnel at half time of their last 16 tie.
Tuesday's result means that River meet either Flamengo or Gremio in the final planned for Santiago, Chile on Nov. 23.
The two Brazilian sides meet on Wednesday's second leg in Rio, with the tie balanced at 1-1 after the first leg in Porto Alegre.
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