Zane Green, who scored 30 not out, struck a boundary off the last delivery of the match to seal a famous victory for the hosts in their first ever T20 clash with their neighbours.
South Africa won the toss and elected to bat but wickets fell regularly as they limped to 134-8, Jason Smith top-scoring with 31. Namibia left-arm seamer Ruben Trumpelmann completed impressive figures of 3-28.
Namibia, who have qualified for next year’s T20 World Cup in India and Sri Lanka, made 138-6 in reply.
"It is obviously not the result you want, but it was a special day for them," South Africa captain Donovan Ferreira said. "We weren't good enough, I don't think we put on a decent score.
"We had soft dismissals and then with the ball, unfortunately, (Gerald) Coetzee getting injured there in his second over. But like I said, all credit to these guys (Namibia), they played really well."
The match marked the return to the South Africa side of swashbuckling opener Quinton de Kock, after the 32-year-old changed his mind about retirement.
But his first international knock in 16 months lasted only four balls as he was dismissed in the first over for one.
De Kock is in South Africa’s squad for a three-match T20 series and three one-day internationals in Pakistan this month.
"You can see what it means for the team," Namibia captain Gerhard Erasmus said. "I think any national team playing in front of their own people, that's how you inspire the next generation to play.
"The guys did it with good skill. (Green and Trupmelmann), they both they operate at a high level. They are consistent performers, and (for Green) it's his birthday, to come off like that, it's such a special moment."