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.
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.
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.
