The Brazilian side beat their Argentine rivals 4-3 on aggregate after the victory at their Beira-Rio stadium.
Internacional qualified for the match as 2010 South American champions and Independiente having won the Copa Sudamericana, the continent's Europa League equivalent, last year.
Damiao, who scored a brilliant bicycle-kick goal in the Brazilian league at the weekend and is reportedly a transfer target for Spurs, put Inter ahead when he beat two defenders and fired a shot with the outside of his right foot across the face of goal and inside the bottom far corner in the 20th minute.
Five minutes later, the 22-year-old latched onto a loose ball on the edge of the box after a defensive mistake and volleyed over goalkeeper Hilario Navarro to give his side a 2-0 lead in the first half.
Independiente came back into the game in the second half with a change of tactics that caught the home side by surprise, changing to a back three and wing backs pushing forward down the flanks.
Left wing-back Maxi Velazquez, who had scored the first goal of the tie when Independiente won the first leg in Avellaneda 2-1, cut inside to take a pass and beat goalkeeper Muriel.
The Brazilians then survived a scare when Muriel parried at point-blank range from Independiente's Colombian forward Marco Perez.
Inter settled the tie with a penalty six minutes from time, converted by left-back Kleber after Navarro had brought down substitute striker Jo.
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