A second-minute goal from Baghdad Bounedjah proved to be the difference as Algeria sealed their second African Cup of Nations title after lifting the cup in 1990.
A fortunate goal for the Greens ultimately sealed the title as Bounedjah's shot struck Salif Sane's leg before landing in the back of the net.
Saivet, who started all of Senegal's knockout ties in this summer's competition, played 75 minutes before the United midfielder was replaced by Galatasaray's Mbaye Diagne as, despite their strong percentage of possession, Senegal were unable to go one better than the 2002 tournament, in which the Lions of Teranga reached the final.
Elsewhere, Newcastle United under-23 defender Oisín McEntee and Republic of Ireland under-19s earned a 2-1 victory over Czech Republic to seal their place in the European Under-19 Championship semi-finals.
Ireland finished in second place of Group B to gain qualification to the last four, where they will meet Portugal in the Armenian capital, Yervean, on Wednesday evening.