South African Aiken and Englishman Fisher both finished the final round at the East London Golf Club on 20-under par to force extra holes.
It was Aiken who emerged victorious on the first extra hole with a 30-foot birdie putt that secured only his third European Tour title and maintained the South African dominance of the event.
The tournament has only ever been won by players from South Africa in its seven-year history, with Aiken joining the likes of Retief Goosen, Louis Oosthuizen and Charl Schwartzel on the honours board.
Aiken started the day four shots behind overnight leader Emiliano Grillo of Argentina, but secured a share of the lead with an excellent four-under 67, the highlight of which was a 12-foot eagle at the third.
Fisher had been ahead of Aiken by two shots at the end of the third round, but he could only card a round of 69 to set up a play-off, with bogeys at the first, seventh and 13th proving pivotal.
A five-over first hole eradicated Grillo's advantage, the South American finishing back in tied fifth on 18 under following a hugely disappointing final round of 73.
There was no such misfortune for Aiken, though, who was delighted to win on home soil after keeping his composure in the play-off.
"I've won a couple of times overseas, but there is nothing like winning in front of a home crowd," Aiken said.
"The South African fans have been unbelievable throughout my whole career so it's nice to finally get one for you guys."
England's David Horsey and American John Hahn finished tied third, with defending champion Darren Fichardt, Jaco van Zyl and Richard Bland joining Grillo in tied fifth.