كتب : Hatem Maher
The Desert Foxes suffered a stunning 3-0 defeat to Malawi in their first game but produced a much-improved display to sink Mali, thanks to a Rafik Halliche header just before the break.
Mali's hopes of booking a last-eight berth now hang by a thread as they have one point from two games, having staged an extraordinary comeback to hold CAN hosts Angola to a 4-4 draw last Sunday.
Algeria, who will play in this year's World Cup finals, have three points.
Angola (1) and Malawi (3) meet in the other Group A game later on Thursday.
Set-pieces
The first-half was a dull affair, with neither side being able to create clear-cut chances.
Defenders had the upper hand before the break but Algeria managed to make the most of their set-pieces prowess to open the scoring on 43 minutes.
A mis-timed jump by Mali keeper Soumbeyla Diakite allowed Halliche to tower and head home Karim Ziani's free kick.
Mali, who lacked creativity and imagination, failed to trouble Algeria's defense in the second half.
They wasted a half-chance to restore parity when Adama Tamboura opted to shoot from a tight angle rather than crossing for his unmarked teammates. His effort hit the side-netting.
Algeria came close to doubling their advantage when a fierce long-range drive from Hassan Yebda narrowly missed the target.
The North Africans held onto their lead to claim their first Nations Cup victory since 2004, having missed out on the previous two editions.