Enyimba once again flopped outside Nigeria, losing a fourth consecutive CAF match to be replaced as Group A leaders by Orlando Pirates of South Africa, who walloped Al Ahly Benghazi of Libya 3-0 in Soweto.
After collecting just one point from a possible nine in the first three rounds, it was win or bust for former African champions Setif and they surged into a two-goal lead by half-time.
Amir Karaoui and Mohamed Amoura scored and Akram Djahnit converted a penalty after half-time to complete an impressive victory which did not lift them off the bottom, however.
Pirates were equally ruthless with Ntsikelelo Nyauza, Tshegofatso Mabasa and Kabelo Dlamini scoring as they maintained an unbeaten run in the section.
The South Africans, who were runners-up in the 2015 Confederation Cup, lead with eight points, Enyimba have six and Benghazi and Setif four each.
Ayman Sfaxi scored, was yellow-carded and created a goal for Wajdi Kechrida as Etoile built a two-goal half-time advantage in a top-of-the-table Group C clash in Sfax.