Ranked 111th in the world by FIFA, Namibia shocked the hosts by taking the lead in the 41st minute before Katlego Mphela's equaliser 20 minutes from time saved Bafana Bafana's blushes.
The result maintained coach Carlos Alberto Parreira's unbeaten record in his second stint at the helm but South Africa should have won the match comfortably after dominating possession.
"We had control of the ball in the first half but the last ball was not good enough to score," said Parreira, who has now led Bafana Bafana to two wins and three draws since replacing fellow Brazilian Joel Santana in November.
"They had one chance and managed to take it and then sat back to defend. In the second half we did not have the patience to have the ball and create opportunities but the moment we got it on the ground we were much better. We should have won."
Namibia's head coach Tom Saintfelt admitted he was pleased with the result but felt that they were unlucky not to hold on to the lead.
"I'm disappointed because we were leading with 20 minutes to go," he said. "We created some great opportunities but I didn't see so many from Bafana Bafana in the first half. We knew it would be hard after the break but it was only one mistake that allowed them to score."
South Africa dominated possession in the first half but were mainly restricted to shots from outside the area, with captain Teko Modise forcing two saves from Athiel Mbaha in the 16th and 30th minutes.
Namibia had looked dangerous on the break and they took the lead four minutes before half-time when Razundara Tjikuzu wrong-footed Bradley Carnell and squared the ball across the area to Maritzburg United's Bester, who beat Itumeleng Khune with a well-placed shot off the post.
Parreira made five substitutions in the first 15 minutes of the second half as Bafana attempted to draw level and Bloemfontein Celtic's Tlou Segolela almost found a way through after the hour mark, only for Mbaha to stretch out a foot and divert the ball away from the goal.
South Africa eventually equalised 10 minutes later when Reneilwe Letsholanyane's pass picked out Bryce Moon on the right and he found Mphela, who fired into the net emphatically for his 10th international goal.