The goals all came in the last 10 minutes of the first half as the pace of the Algerians and the accuracy of their passes cut open the Tanzanian defence almost at will.
Having already booked their place in the last 16, the Desert Warriors coach Djamel Belmadi made nine changes to the side that beat Senegal in their last game, with Riyad Mahrez having to settle for a place among the substitutes.
UEFA Nations League
Mourinho doesn't want ‘scared’ Southgate’s job - The Warm-Up
Hichem Boudaoui had already missed a good chance to give Algeria the lead when Islam Slimani struck his 27th international goal as the Leicester striker latched onto Adam Ounas' pass before finishing coolly past Metacha Mnata after 34 minutes.
Ounas had a goal of his own five minutes later as he took Slimani's pass to fire low beyond Mnata.
Hassan Ramadhan - Haris Belkebla - Tanzania - Algeria - Africa Cup of Nations
Image credit: Getty Images
Algeria had a third before half-time as Tanzania's defence fell apart once more to allow Ounas to round Mnata for his second.
The final set of Group C results mean that Algeria will face Ivory Coast in the last 16, with runners-up Senegal - 3-0 winners over Kenya on Monday - taking on Uganda.
Barca may let Perez go to sign Moreno - Paper Round
Renard quits as Morocco coach