The first goal of the game came after just a minute as Porto's Yacine Brahimi fired high into the net after a neat one-two with Islam Slimani on the edge of the area.
Riyad Mahrez, who plays for English Premier League side Leicester City, doubled the lead on the stroke of half-time. He picked up a superb through ball from Sofiane Feghouli before turning inside a defender and finishing with a low shot.
Mahrez then turned provider as his cross was met by Slimani's head to confirm Algeria's place at the Nations Cup finals.
Earlier Ethiopia, despite playing the last 30 minutes with 10 men, avenged their loss on Saturday at home to Mali with a surprise 3-2 win in Bamako. Bakary Sako, who plays in the English Championship, gave the hosts the lead after 32 minutes but that was cancelled out just four minutes later by Egypt-based Oumed Oukri.
Getaneh Kebede was hero and villain for Ethiopia - first giving his side the lead on the stroke of half-time but then getting himself sent off 12 minutes after the break.
Mali made the extra man tell and equalised through Mohamed Yatabare with 20 minutes left to play, but in the final minute defender Abebaw Butako scored to give his side a vital three points.
The results mean Algeria have a maximum 12 points guaranteeing them a top two finish, Mali stay second despite losing on six points while Malawi and Ethiopia both have three.
The top two from each group and the best third-placed side qualify for the tournament in Morocco.
Wednesday results:
| Cameroon 2-0 Sierra Leone | Togo 1-0 Uganda | Angola 4-0 Lesotho |
| Ghana 3-1 Guinea | Nigeria 3-1 Sudan | Zambia 3-0 Niger |
| Egypt 2-0 Botswana | Ivory Coast 3-4 DR Congo | Cape Verde 1-0 Mozambique |
| Burkina Faso 1-1 Gabon | Mali 2-3 Ethiopia | South Africa 0-0 Congo |
| Tunisia 1-0 Senegal | Algeria 3-0 Malawi |