The teams finish tied in a helter-skelter end to the regulation 20 overs a side after South Africa collapsed from a position where victory seemed certain and had to scramble a single off the last ball of its chase to tie the scores.
As the South African tailenders sneaked through for that tying run, Sri Lankan wicketkeeper Niroshan Dickwella missed a straightforward throw at the stumps that would have given Sri Lanka victory.
South Africa clawed its way to 134-8 to force the Super Over after Sri Lanka had earlier posted 134-7.
South Africa batted first in the Super Over and made 14, with David Miller cracking a six and a four off Sri Lankan captain Lasith Malinga.
South Africa chose legspinner Imran Tahir to bowl Sri Lanka's Super Over and he conceded just five — although that still included two dropped catches and two wides.
That was only half the story of a thrilling match.
South Africa threw away its winning position and only just managed to tie and Tahir was the savior for the home team then, too.
He came in to bat with South Africa needing two to win and one to tie.
He inside edged straight to Dickwella behind the stumps but Tahir and Dale Steyn still scuttled through for the tying run. Dickwella's throw from close range missed the stumps and the ball also then hit Tahir, who was sprinting down the pitch to complete the run.
South Africa should have won comfortably much earlier after Miller (41) and Rassie van der Dussen (34) put the pedal down in the 15th over of the run chase, with Miller cracking three fours and a six and taking 20 runs off the over by Isuru Udana.
Van der Dussen hit a six and a four in the next over and South Africa needed just 18 runs from 24 balls after that.
Malinga brought himself on to bowl and that sparked South Africa's collapse.
Van der Dussen was caught and Miller ran himself out going for a needless second run in the space of two balls of Malinga's over. South Africa went on to lose five wickets for 15 runs, two of them run outs.
Even when South Africa needed six runs off the last two overs, and four off the last over, it still couldn't do it.
Malinga bowled brilliantly, conceding just one run and bowling Kagiso Rabada in the penultimate over.
Needing three off two balls, JP Duminy was run out going for a crazy second run to set up the last-ball scramble.
After he and Tahir managed to tie the scores, Steyn smiled and shook his head, summing up the game.