Aiken birdied the first extra hole at East London Golf Club after he and Fisher had finished tied on 20 under par, joining compatriots Charl Schwartzel, Louis Oosthuizen (twice) and Darren Fichardt in lifting the trophy.
Fisher narrowly failed with a birdie putt on the 18th to win in regulation, but then missed the green when the players returned to the same hole for the play-off and was facing a 15ft par attempt before Aiken made sure of victory by holing from 35ft.
It was the 30-year-old's first European Tour win on home soil after previous victories in Spain and India, not to mention the first with his wife Kate acting as his caddie, with his regular bagman in America on business.
"I've been waiting for this for quite some time," said Aiken, who was second to Schwartzel in the inaugural Africa Open in 2010. "I have won a couple of times overseas but there is nothing like winning in front of a home crowd. The South African fans have been unbelievable throughout my whole career, so it's nice to finally get one for you guys.
"Thanks so much to my wife who helped me on the bag this week for the first time; this could be a bit of trouble because we might have to do it again!"
As well as finishing runner-up in 2010, Aiken had recorded three top-15 finishes at East London and praised the undulating layout, which at 6,632 yards is the shortest on the European Tour.
"East London is a fantastic golf club, it's an old club and it just shows a course doesn't need to be long for it to play interestingly," Aiken added. "You have to think your way around this golf course, it's not just get up on every tee and hit driver.
"You have to really position the ball well, there is a lot of bush out there that can catch you. It's very much a strategic course and I always love coming back here. I have done well the last four years and it's so great to finally get this trophy under my belt."
Aiken had finished fifth in his last two events in Qatar and Johannesburg, adding: "I got sick on Wednesday last week and it got progressively worse, I just didn't have much energy on Sunday.
"You have days like that but you have to take the positives out of every week and the last few weeks I have finished in the top five, the golf has been good and it was only a matter of time until something happened. I just stayed very patient this week and it just shows what patience can do."
Aiken had carded a closing 67 and Fisher a 69, with the tournament blown wide open when overnight leader Emiliano Grillo ran up a quintuple-bogey nine on the first.
Grillo held a two-shot lead thanks to a brilliant 62 on Saturday, but the 21-year-old Argentinian had already taken a penalty drop from an unplayable lie when he chipped his fourth shot into a greenside bunker, from where he needed two attempts to escape.
His sixth shot had rolled back off the green however and after chipping up to seven feet, he needed two putts to complete an extraordinary opening hole and drop his first shot since his 15th hole on Thursday.
To his credit, Grillo battled back from a front nine of 43 to birdie the last five holes and claim a share of fifth place on 18 under alongside Richard Bland, Jaco van Zyl and defending champion Darren Fichardt.
England's David Horsey birdied four of his last six holes to shoot a final round of 65 and claim a share of third on 19 under alongside American John Hahn.