Zambia shaded the action in Lusaka, though South Africa had enough chances to win the game, and were ultimately undone by another poor piece of defending.
The first half was one of few chances, but Luther singh blazed a free-kick narrowly over the bar and Sibongakonke Mbatha should have done better when he volleyed over in acres of space.
Kobamelo Kodisang forced a good save from Zambian goalkeeper Mangani Banda from a 35-yard free-kick, and then the best chance of the game was missed by Mbatha.
He had time and space to pick his spot, but blazed wildly over the bar with the goal at his mercy.
Zambia had been reduced to shots from range in the game but near the end of 90 minutes fashioned some more clear-cut chances.
Patson Daka blocked clearance from South African defender Notha Ngcobo and almost got lucky as the ball bounced onto the post and away to safety.
And Daka then had a shot inside the box in injury-time that forced a smart save from South African keeper Mondli Mpoto.
The match went to an extra 30 minutes and Zambia had a magnificent chance to grab the opener when Enock Mwepu found himself with an open goal, but blasted the ball over the bar from six yards for what was a shocking miss.
The match was briefly stopped a minute before halftime in extra-time when police outside of the stadium fired teargas and the fumes wafted into the venue, leaving the players spluttering.
When the game resumed it was Zambia who grabbed the initiative and the winner.
A free-kick on the right-hand edge of the South African box was headed home by Chilufya and South Africa could not find an equaliser.
TEAMS
Zambia: M. Banda, Nyondo, Chiluya, S. Sakala, Mwepu, E. Banda (Kalunga 79'), Mayembe, Chilufya, F. Sakala, Daka, Musonda.
South Africa: Mpoto, Ngcobo, Mukumela, Malepe, Mthethwa, Meyiwa (Shopane 113'), Mokoena, Singh, Margeman (Mbule 101'), Mbatha, Mayo (Kodisang 53').