Second-half goals from Gabriel Mercado and German Pezzella at the Estadio Monumental Antonio Vespucio Liberti in Buenos Aires gave River a 3-1 victory on aggregate in the two-legged final.
Full-back Mercado broke the deadlock and put the Argentines ahead on aggregate in the 55th minute, before centre-back Pezzella doubled the lead four minutes later as River won their first international title in 17 years.
River clinched the now defunct Supercopa Sudamericana title in 1997.
After last week's 1-1 draw in Colombia, River returned home with confidence thanks to Leonardo Pisculichi 66th-minute equaliser.
But the prospect of extra time and penalties - with the away goals rule not used in the final - appeared more and more likely after a scoreless first half in the Argentine capital, despite River's dominance.
The deadlock, though, was eventually broken by the Argentine Primera Division giants 10 minutes into the second half.
Mercado made room ahead of his opponent and glanced Pisculichi's corner past Nacional goalkeeper Franco Armani.
It got better for the home side four minutes later, with Pisculichi the provider yet again.
Pisculichi's corner was headed home powerfully by Pezzella, who directed the ball into the same area of the net as Mercado.
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