The Black Eagles won the last-32 tie 3-1 on aggregate after coming from behind in Banjul three weeks ago to force a 1-1 first-leg draw.
Midfielder Toufik Zerara gave Setif a mid-first-half lead and defender Farid Mellouli added a second goal three minutes into the second half at Stade 8 Mai.
Setif can expect tougher opposition in the round of 16 where they will tackle Moroccans Raja Casablanca or South Africans Kaizer Chiefs.
Raja won the first leg 1-0 in Durban and are favoured to advance after the return match in Casablanca on Sunday.
Setif are hoping to emulate Nigerians Enyimba, Egyptians Al-Ahly and Congolese TP Mazembe by successfully defending the title.
Fellow Algerians USM Alger also progressed after drawing 1-1 with Senegalese AS Pikine at Stade Demba Diop in Dakar.
The tie was all but over as a contest after the Algiers outfit won 5-1 at home in mid-March despite having a player red-carded midway through the second half.
El Hadji Alioune Sow gave Pikine a first-half lead at home and Hamza Koudri levelled 11 minutes from time.