Baghdad Bounedjah's shot took a huge deflection off Salif Sane and looped over goalkeeper Alfred Gomes.
Senegal, who have never won the competition, were awarded a penalty for handball in the second half but it was overturned after a VAR review.
Algeria closed out the rest of the game to win their first title since 1990.
Senegal's players collapsed on the pitch in tears at the final whistle.
Liverpool forward Sadio Mane, who said before the game he would swap his Champions League winners medal for Africa Cup of Nations success, looked disconsolate as Algeria players celebrated around him.
"Without the players I am nothing," said Algeria boss Djamel Belmadi. "They are the main ones. I suppose the staff played its part in guiding the players but they applied the instructions incredibly well."
Senegal, making only their second appearance in the final since 2002, dominated for large periods but struggled to make the most of their possession.
M'Baye Niang was at the centre of two of their best chances as he flashed a fierce drive over the bar just before the break, and rounded keeper Rais M'bolhi early in the second half only to shoot wide from a tight angle.
M'Bolhi also did well to palm over a stinging effort from Youssouf Sabaly.
The decisive moment for Senegal was the reversal of the decision to award a penalty on the hour mark.
Ismaila Sarr's cross was blasted straight at Adlene Guedioura's arm, referee Neant Alioum pointed to the spot, but, just as the Senegal players started celebrating the decision, he quickly indicated that a VAR review was under way.
After watching the replays on the pitch-side monitor, which clearly showed Guedioura's arm being by his side, Alioum reversed the decision.
Although the decision was correct, the result was harsh on Senegal, with Algeria managing only one shot on goal.
