Hassan Yebda netted a seventh-minute penalty for the home team to settle the match, leaving all four teams i...n Group D locked on four points from three games.
Algeria, a 2010 World Cup qualifier, clinched a desperately needed win after beginning its campaign with a draw and a loss.
With three matches left, Central African Republic is still the surprise leader on goal difference from Tanzania, Morocco and then Algeria.
The Algerians defended their lead resolutely following Yebda's early spot kick.
The African Cup will be held next year in Gabon and Equatorial Guinea.
> The Canadian Press
