After the first leg in Kinshasa ended 2-2, it was the North Africans who were crowned kings of African club football for the second time in their history after a 1-1 draw in Blida.
Setif adopted a cautious approach in the first half, knowing that the Congolese are good away from home.
After a goalless first half, Setif took the lead five minutes after the break through Younes Sofiane as he scambled at the far post to turn home a cross from the right, but just four minutes after that, Lema Mabidi pulled Vita level again with a cracking strike from 20 yards out.
Vita still had to score another goal to avoid defeat after Setif scored two away-goals in the first leg but were unable to do so as Setif survived a tense final few minutes, meaning the Algerian side won on the away-goals rule after a 3-3 aggregate score.
It is the second title for Setif after their first African Champions Cup win in 1988. They are also the first Algerian club to win the compeition since rivals JS Kabylie in 1990.
Setif will receive $1.5-million and represent Africa at the 2014 FIFA Club World Cup in Morocco in December.
