Furyk ended the event at 6-under-par 282. He was joined in the extra session by 2004 champion Retief Goosen (72), third-round co-leader Adam Scott (73) and Darren Clarke, whose closing 69 was one of just two rounds in the 60s on Sunday.
Luke Donald posted a two-under-par 70 to finish alone in fifth place at 5-under 283. Tim Clark, who shared the third-round lead with Scott and Angel Cabrera, struggled to a 3-over 75 to end in sixth at minus-4.
Early on, Furyk moved into a share of the lead with a birdie at the second. He led alone after Scott bogeyed the third, then ran off six straight pars before a birdie on No. 9 moved him to minus-8.
Furyk bogeyed the 12th at Gary Player Country Club, but came right back to birdie No. 13. However, he tripped to bogeys on the 15th and 18th to fall back to minus-6.
On the first extra hole, Goosen fell out of the playoff. On the second playoff hole, it came down to Clarke and Furyk. Clarke was guaranteed a par, but Furyk took things into his own hands.
Furyk's second shot rolled off the back of the green leaving a delicate, downhill chip. No matter, he played a perfect shot into the cup for birdie and the win.
Masters runner-up Chris DiMarco took seventh place at even-par 288 after a 1-over 73 in the final round. Cabrera, who also led after the second round, could not recover from his triple-bogey on the 18th Saturday. Those bad feelings lingered as he stumbled to an eight-over 80 to finish at plus-one.
Ernie Els, who played this week for the first time since injuring his knee after the British Open, closed with a 3-over 75 in breezy conditions to finish the event at two-over-par 290.
Kenny Perry carded the round of the day with a 4-under 68. He took 10th place at 3-over-par 291, with Sergio Garcia (plus-4) and Stewart Cink (plus-10) closing out the field.