From Bethuel Muzeu's clinical delivery, Deon Hotto headed home past Bechir Ben Saïd to secure a shock win for Namibia.
In addition, Tunisia, the hosts of the 1994 Africa Cup of Nations, kicked off the tournament with a 2-0 defeat to Mali in Tunis.
The Tunisians fell behind from a clinical piece of play, as Kamory Doumbia delivered a brilliant pass before Lassine Sinayoko stroked into the far corner to give Mali the lead.
Namibia was the first to make opportunities, but following a handball by Deon Hotto in an attempt to block Thapelo Morena, a penalty was given, and Percy Tau scored.
The situation became increasingly more favorable for the South Africans when Themba Zwane clinically finished from a pass from Morena in the 25th minute.
The nations also met three other times: 2000 in Accra, Ghana, when South Africa defeated Tunisia 4-3 in a penalty shootout to finish third in that tournament in.
Tunisia's Ali Zitouni scored twice, including an 89th-minute goal to force extra time, but missed the final penalty kick in the shootout; 2006 in Alexandria, Egypt, with Tunisia winning 2-0 in the teams' second match in the group stage, a result that confirmed South Africa's elimination from the 2006 Africa Cup of Nations with a game to go; and 2008 in Tamale, Ghana, with Tunisia winning 3-1 in the teams' second match in the group stage.
However, with the match becoming increasingly dire for Tunisia, the Tunisians were forced to pour everything forward and, as a result, they almost fell to counterattack traps by South Africa, notably a failed effort by Sphephelo Sithole.
Haythem Jouini had a chance but his nodd over from a glorious position went wide, as the result ended goalless, enough for South Africa but too late for Tunisia.
However, as the game went to final minutes, Namibia dug deep to prevent any further Malian attempts as both teams were satisfied with a goalless draw.