Eduwo netted twice in the first half and Rami Bedoui scored early in the second half to complete an impressive Group C matchday four victory over the Nigerian club near Tunis.
Success took Club Africain to the top of the table with nine points, ahead of Dreams of Ghana on head-to-head records. Rivers have six points and Academica Lobito of Angola none.
The closest Nigeria have come to winning the African equivalent of the UEFA Europa League was in 2005 when Dolphins lost to FAR Rabat of Morocco in the final.
Dolphins merged with Sharks in 2016 to form Rivers United, who are based in the southeastern city of Port Harcourt.
African debutants Dreams hammered Lobito 4-0 in Kumasi with three of the goals coming after half-time, including one from consistent scorer Abdul Issah.
The first Confederation Cup final in 2004 was an all-Ghana affair, with Hearts of Oak defeating Asante Kotoko, but no club from the country has come close to lifting the trophy since.
Matchday four offered three clubs, title-holders USM Alger of Algeria and former winners Zamalek of Egypt and Renaissance Berkane of Morocco, chances to secure quarter-finals places.
USM and Zamalek succeeded while Berkane need one point from two fixtures to move closer to a record-equalling third title.
A 0-0 draw with Modern Future of Egypt in Cairo sufficed for Group A leaders USM, who edged Young Africans of Tanzania on away goals in the 2023 final.
Zamalek also drew 0-0, away to Esperanca Sagrada of Angola in Luanda, and the point assured them of qualification from Group B.
Youssef Zghoudi equalised for Berkane in a 1-1 Group D draw away to Diables Noirs of Congo Brazzaville, who snapped a three-match losing streak.
Nigerian Etiosa Ighodaro scored to earn SuperSport United of South Africa a 2-1 home win over Al Hilal Benghazi of Libya after a Group A clash in which red cards reduced both sides to 10 men.
AFP
