Garcia closed with a 2-under 70 despite a bogey on the first hole that wiped out his one-stroke overnight lead. He came right back with consecutive birdies from the third to get to 13 under.
The Spaniard dropped another stroke at the sixth. However, he recovered that stroke on No. 8 at Gary Player Country Club when he rolled in a birdie putt.
Around the turn, Garcia climbed to 14 under with a birdie at the 10th. He parred in from there.
Goosen was able to keep pace with Garcia as he birdied the second and sixth. He birdied the ninth and 10th to climb 15 under and sole possession of first place.
The South African, however, bogeyed the 14th hole, which he had birdied the first three rounds. The bogey dropped Goosen into a tie for the lead, and he parred in from there. Both players had a chance for birdie at the last, but neither could convert.
On the first extra hole, No. 16, Garcia found magic for the second time. This time around, he rolled home a 20-footer for birdie and the $1.2 million first-place check. Garcia chipped in for birdie on the same hole at this event in 2001 to knock off Ernie Els, also in a playoff.
Vijay Singh capped an outstanding year as he finished in third place at 11-under-par 277. Darren Clarke posted the round of the day of 5-under 67 to climb into fourth place. He finished a 10-under-par 278.
Jerry Kelly and Kenny Perry, a pair of American Presidents Cup players, shared fifth place at 7-under-par 281. Chris DiMarco and Adam Scott, both of whom also played in the Presidents Cup, tied for seventh at 6-under-par 282.
Ernie Els, the 2002 defending champion and three-time winner, closed with a 3-under 69 to climb out of last place. He finished at 2-over-par 290 in 17th place.