Baghdad Bounedjah put the Algerians ahead in the 19th minute with a well-taken goal but clumsy defending cost them when Nabil Bentaleb committed a foul and gave away a penalty, converted by Angola substitute Mabululu in the 68th minute.
Algeria have now failed to win in four matches at the Cup of Nations finals since lifting the trophy in Cairo.
They made a shocking attempt to retain the title at the last edition in Cameroon two years ago, going home early with one point from the group games and losing to tiny Equatorial Guinea.
They looked keen to expunge those memories and dominated the early stages with a crisp passing game and incisive running.
They went ahead when Bounedjah burst between Angola's two centre backs to collect a long ball over the top of the defence and finish with a powerful shot.
Six minutes later he had the ball in the net with a spectacular bicycle kick, but was marginally offside and the effort was ruled out. Had it counted, it would have been an early contender for goal of the tournament.
However, Algeria failed to press home their advantage and gave up their lead 22 minutes from time.
Bentaleb's clumsy challenge from behind on Mabululu, kicking him on the calf while trying to clear the ball, brought Angola back into contention and was their only real chance of the game.
Mabululu almost botched the kick as he hit the underside of the bar with the ball just crossing the line.
Algeria made a muted effort to try and restore their advantage and had a real opportunity seven minutes into stoppage time but a free kick from Fares Chaibiwas well saved.