In a tournament cut to 36 holes and on a Royal Durban course reduced to a par-65 because of saturated fairways, Jamieson shot a second-round 57 and then beat England's Steve Webster and Spaniard Edoardo de la Riva in a play-off.
De la Riva bogeyed the first extra hole and then, in fast-fading light, Webster, the only one of the trio to have won on the circuit before, did the same when they returned to the 18th tee.
Jamieson, whose previous best finish was third, will not go into the Tour record books for his 57, however. Because of the course conditions it will not officially count, but that will not matter to the 29-year-old ranked 167th in the world.
He was not even in the top 60 after his opening round of 66 and admitted afterwards: "Starting the day I probably didn't think I would be standing here holding the trophy."
All three players involved in the play-off finished their rounds by lunchtime and had to wait all afternoon to see if anybody could beat their seven-under totals of 123.
South Africa's Tim Clark had the best chance, but double-bogeyed the 17th when joint leader.
De la Riva, who less than a fortnight ago came through the Tour qualifying school in joint ninth place, was left to rue not only failing to get up and down from a bunker in the play-off, but also a closing bogey in his second-round 61.
Webster, who had the second of his two victories in Portugal five years ago, produced a 60 and almost clinched victory on the first extra hole when his 30-foot birdie putt came up just short.
Next time round, though, he could not recover from pulling his drive into thick rough.
Earlier, Jamieson could have won it outright on the 305-yard ninth - his last - when he drove the green, but just missed a 12-foot eagle attempt.
He had earlier gone to the turn in a five-under 26 that included four birdie twos.
"I knew I needed a fast start and was lucky enough to get that," Jamieson added after also being presented with a framed drawing of Mandela.
"It's an honour to win a tournament like this. Getting your name on any European trophy is a fantastic achievement, but it's a bit more special with someone like Nelson."
Joint fourth a stroke behind were Clark, German Max Kieffer, Dane Morten Orum Madsen and England's Matthew Nixon.