The Algerian side claimed a battling 2-1 win over TP Mazembe in the first leg, with Abdelmalek Ziaya's late solo goal securing victory.
And Ziaya struck again for Setif to break the deadlock after just nine minutes on Sunday, nodding in a chipped cross to give Mazembe an early mountain to climb.
However, the hosts battled back and ended up 2-1 ahead by half-time as Daniel Adjei Nii headed in from close range after Sofiane Khedairia palmed a free-kick on to the post and then Salif Coulibaly directed Solomon Asante's corner in.
Jonathan Bolingi looked to have scored the winner just after the break as he headed Mbwana Samatta's cross into the bottom-right corner.
Setif had the last laugh, though, as Sofiane Younes grabbed the all-important second away goal 15 minutes from the end, as his right-wing cross went straight over Muteba Kidiaba and into the net.
Mazembe piled the pressure on in the final stages, but ultimately they were unable find a fourth goal and the Algerian side go through to the final to face Vita Club, following their 4-2 aggregate win over Sfaxien.
