Spaniard Garcia, who had not won a title since the 2002 Korean Open, holed a 15-foot birdie putt at the first extra hole after both players had finished level on 14-under 274 at the par-72 Gary Player Country Club.
The 23-year-old Garcia, who claimed the $1,2 million first prize, had closed with a 70 while 2001 U.S. Open champion Goosen carded a final-round 69.
Fiji's Vijay Singh returned a 69 to finish third at 11-under 277 with Northern Ireland's Darren Clarke, who shot a best-of-the-day 67, a further shot back in fourth.
It was the second time Garcia had won the tournament at the par-three 16th, having chipped in for a birdie from the fringe of the green to beat South African Ernie Els in a playoff for the 2001 title.
"Retief turned to me after I sank the putt and said: 'You like this hole, don't you?'" Garcia said.
Sunday's victory confirmed that the Spanish Ryder Cup player has finally turned the corner after a year of patiently remodelling his swing under the watchful eye of his coach and father Victor.
"I really feel like my swing is good and getting better and better and I hit some beautiful shots out there," Garcia said.
"I've been fighting hard all year long and I really wanted it today, but sometimes you try to hard. I had to relax."
Last week, the Spaniard threw away a two-shot lead at the Dunlop Phoenix tournament in Japan, carding a final-round 78 to slip back into fourth.
WINNING FEELING
"I tried to win so badly in Japan but I let myself down," he said. "It is good to finally get that winning feeling back."
Garcia started the day one stroke ahead of the field at 12 under par, but bogeyed the first after shanking his nine-iron approach 40 yards right of the green.
"I swung quickly at the ball because I was excited and nervous, but I just had to put it behind me," said the Spaniard.
"I calmed down and said to myself that anything I hit today cannot be worse than that shot."
South African Goosen, who began the final round a shot behind Garcia, birdied the par-five second after hitting a three-wood to 12 feet. He missed the eagle putt but had a tap-in for birdie.
However Garcia finally found his range on the par-four third, sinking a 20-foot birdie putt, and followed that by picking up another shot at the par-three fourth, where his tee shot finished six feet from the hole.
Goosen pulled ahead with a birdie on the par-four sixth, where he nearly holed his approach, but Garcia hit back with a birdie of his own at the difficult par-four eighth.
The smooth-swinging Goosen again took the outright lead on the par-five ninth, needing only a five-iron approach into the island green for a two-putt birdie.
Both players birdied the 10th before Garcia closed with a run of eight consecutive pars. Goosen, however, bogeyed the par-five 14th to drop back into a tie for the lead at 14 under.
The South African had a chance to clinch victory at the last, but missed a 10-foot putt for birdie to take the tournament into extra time.
