Algeria made a poor defence of their Cup of Nations title in Cameroon this year and were dramatically beaten in the last minute of the World Cup playoffs.
However, they beat Uganda at home on Saturday and travelled to Dar-es-Salaam to secure another 2-0 victory on Wednesday.
Ramy Bensebaini scored on the stroke of halftime after Tanzania had several early chances and Mohamed Amoura added a second with a stinging shot from close range in the last minute of the Group F game.
Algeria are now well placed to secure early qualification as they sit on six points, with Niger on two after holding Uganda to a 1-1 draw in Kampala on Wednesday. Uganda and Tanzania have one point each.
It could also spell an end to Hector Cuper's spell as coach of DR Congo, who failed to reach the last Cup of Nations finals.
Mauritania, who beat Sudan 3-0 last weekend, moved to the top of Group I with a goalless draw in Franceville against Gabon.
Mozambique pulled off a surprise 1-0 win at Benin with a first-half strike from Geny Catamo in Group L while Antoine Makoumbou got the only goal as Congo beat Gambia in Brazzaville to get their first points of the Group G campaign.
The top two teams in each of the 12 groups qualify for the finals, except in Group H where hosts Ivory Coast are competing. In that group, only one team other than the Ivorians will qualify.