All three goals were scored by the Nigerians, including defender Segun Oduduwa putting the ball in the wrong end of the post.
The night belonged to Warri Wolves midfielder Oghenekaro Etebo, whose two brilliant moments sealed the Afcon title for Samson Siasia's men.
Nigeria head coach Siasia named 2015 Under-17 World Cup star Victor Osimhen in the startlist for the first time while captain Azubuike Okechukwu returned to the side after missing the semifinals against Senegal following suspension.
Algeria coach Pierre-Andre Schurman stuck to 10 of the players who featured in their previous four games of the tournament with Abdelhakim Amokrane being the only man with two appearances in Senegal among the starters.
The West Africans were on top of the game from the start and should have taken the lead just 27 seconds into the game when Osimhen tamely volleyed at Algeria goalkeeper Abdelkadir Salhi.
Nigeria continued to press high up, and in the 11th minute Osimhen cushioned the ball with his chest off his marker but failed to make his final touch count.
Two minutes later, Etebo's pace unlocked the Algerian backline and he was upended by Ayoub Abdellaoui in the box and the referee Hamada Nampiandraza pointed to the spot.
Etebo dusted himself off and converted the spot kick to give Nigeria a 1-0 lead.
A minute past the half hour mark, Oduduwa turned in Zinedine Ferhat's cross into his own goal to level the scores.
Five minutes before the break, Etebo's pace was once again too much to handle for the Algerians. He ghosted past his markers before slotting past Salhi in goal.
The business end of the game was quite a balanced affair as the Algerians forced Daniel into making saves. Amokrane and Oussama Chita came closest.
The best chance of the second half was from the spot and to Algeria. However, Daniel saved Ferhat's spot kick in the 69th minute.
Nigeria held off the Algerians in the last 20 minutes and not even Mohamed Benkhemassa's effort from range in added time could beat the impressive goalkeeper Daniel.