Djamel Belmadi's side needed a sensational last-gasp Riyad Mahrez winner to beat Nigeria in the last four, but it was a scrappy early strike that decided this clash as Baghdad Bounedjah benefited from a huge deflection.
Further chances were few and far between in an ill-tempered affair as Algeria withstood almost constant pressure and also saw a Senegal penalty award overturned with VAR.
The single goal ultimately proved enough to hold on, Algeria triumphing on foreign soil for the first time to add to their 1990 success as hosts.
Algeria's fortuitous opener arrived inside two minutes. Bounedjah cut inside from the left and saw a powerful strike loop up off the lunging Salif Sane, dropping over static goalkeeper Alfred Gomis into the top-right corner.
Senegal responded well, getting into dangerous positions and winning countless free-kicks, mainly through Sadio Mane, but their final ball was repeatedly found wanting.
Frustrations threatened to boil over late in the first half, with Mane escaping punishment for an off-the-ball shove on Sofiane Feghouli, although M'Baye Niang went close with a fizzing long-range drive.
The two sides came together to confront the referee at the break - Senegal bemoaning a non-penalty award for Ismaila Sarr - and Algeria substitute goalkeeper Alexandre Oukidja went down claiming contact in the ensuing fracas.
And Senegal were further infuriated on the hour mark when a spot-kick initially awarded as Adlene Guedioura blocked Sarr's cross with his arm was struck off following a VAR review.
Niang rounded Rais M'bolhi but could only blaze high and wide, before the goalkeeper turned Youssouf Sabaly's blast over the crossbar.
Aliou Cisse's side kept pushing, yet there was no way through and Algeria clung to a scarcely deserved victory.