The victory followed a surprise 3-0 defeat for the World Cup-bound north Africans in their opening match against Malawi on Monday.
"I think we started off on the wrong foot but we managed to increase our confidence and the goal was crucial," Algeria coach Rabah Saadane told reporters.
Halliche climbed above Mali's defence to head home a free kick from Karim Ziani two minutes before the interval.
Mali had needlessly given away the free kick after a clumsy challenge from Bakary Soumare on Yacine Bezzaz.
The defeat left Mali on the brink of elimination despite having an array of top players from leading European clubs. They have a single point from two matches at the tournament.
The likes of Barcelona's Seydou Keita, Momo Sissoko of Juventus and captain Mahamadou Diarra, who plays for Real Madrid, proved ineffective for a tired-looking Mali.
Frederic Kanoute, left out of the team after struggling with a cold, failed to inject any new impetus when he came on as a substitute after 62 minutes.
Diarra was also cautioned for a second successive game and will sit out Mali's last match against Malawi in Cabinda on Monday.
"This was a key game. We knew it would be difficult but Algeria were lucky to score the first goal and they won," said Diarra.
"We are now forced to win the next game."
Diarra's team looked spent after the exertions of the opening match on Sunday when they conjured four late goals to draw 4-4 with hosts Angola in a dramatic start to the three-week event.
Mali had several half chances early on but Algeria found an extra gear after taking the lead and might have scored more in the second half.
Hassan Yebda missed a good chance in the 70th minute after being set up by Abdelkader Ghezzal and Ziani went narrowly wide with a free-kick.
