The teams played out a 1-1 draw in last week's first meeting in Buenos Aires, a result which pleased the Brazilian side more than the Argentinian outfit, and two second-half goals from Emerson ensured Corinthians finished the job in Sao Paulo.
The victory secured not only a maiden Libertadores title for Tite's Corinthians, who went through the competition unbeaten, but also a place in December's FIFA Club World Cup in Japan.
A scrappy first half at the Estadio Pacaembu took a turn for the worse for Boca in the 32nd minute, when goalkeeper Agustin Orion collided with team-mate Leandro Somoza and was forced to leave the pitch with a knee injury.
Sebastian Sosa, who lost the 2011 Libertadores final with Penarol against Santos, replaced Orion between the posts but was powerless to prevent Emerson from opening the scoring eight minutes into the second half. Alex's free-kick into the box was deflected by the head of Jorge Henrique towards Danilo, whose neat flick set up Emerson for a cool right-footed finish.
Emerson ends the contest
Boca coach Julio Falcioni made attacking substitutions by replacing midfielder Pablo Ledesma with forward Dario Cvitanich in a bid to get back on level terms, but they were soon hit with a sucker-punch as a bad mistake from defender Rolando Schiavi allowed the hosts to double their lead. Schiavi misdirected a pass straight to Emerson, who ran more than 40 metres before unleashing his shot past Sosa.
"I am very happy because we know the history Boca Juniors have in worldwide football and in the Copa Libertadores," Emerson told Fox Sports. "Our crowd represents 33 million fans. Since this year's Libertadores started, we have dreamt of clinching the title. We were all in need of this achievement."
Danilo, a previous Libertadores winner with Sao Paulo, said: "We totally deserved this. We did not lose any games. It is extraordinary for us to win this title, which Corinthians had never won in the past."
Defender Leandro Castan added: "We have made it into the history of the club. Maybe it was my last game at Corinthians but I will announce it on Friday. Now, it's time to celebrate. Boca were great rivals."
Corinthians became the ninth Brazilian team to lift the Copa Libertadores, joining Santos (1962, 1963 and 2011), Cruzeiro (1976 and 1997), Flamengo (1981), Gremio (1983 and 1995), Sao Paulo (1992, 1993 and 2005), Vasco da Gama (1998), Palmeiras (1999) and Internacional (2006 and 2010).