Bounedjah gave Algeria a dream start in the second minute when his deflected shot looped over Senegal goalkeeper Alfred Gomis, and it proved enough for the 1990 champions to lift the trophy for the first time.
It was the first title-decider to feature two African coaches since 1998, with Algeria boss Djamel Belmadi completing a whirlwind 12 months at the helm after inheriting a side that failed to make it out of the group stage two years ago.
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With defensive rock Kalidou Koulibaly suspended for Senegal, Salif Sane deputised at the back and Ismaila Sarr was recalled in attack, while Belmadi kept faith in the same side that overcame Nigeria with an injury-time free-kick from Riyad Mahrez.
Senegal had understandably feared the absence of Napoli star Koulibaly, banned after two bookings in the knockout rounds, although the towering Sane was desperately unlucky as Algeria grabbed the lead with scarcely a minute played.
As Bounedjah took aim from 20 yards his effort smacked off Sane and arced high into the air before dropping underneath the crossbar and beyond a static Gomis, sparking delirious celebrations from both players and fans, some of whom arrived for the final on military planes provided by the Algerian government.