'I played with Ernie once before in a World Cup and it's nice to win it with him,' said Goosen, who teamed up with Els to tie for sixth place at the 1993 event in Florida. 'It's been a great week.'
Denmark's Soren Hansen, who watched with mouth agape as teammate Thomas Bjorn rolled in a clutch birdie from 12 feet at the 18th in regulation, had a chance to extend the playoff but missed an eight-foot putt to save par.
The United States and New Zealand also qualified for sudden death but were eliminated when they failed to birdie the first extra hole.
Els knocked a wedge to 15 feet at the second extra hole, the par-4 14th, setting up a two-putt par that won the playoff, only the second in the history of the World Cup.
Els and Goosen, a duo with three U.S. Open titles between them, will split $1 million from the $3 million purse.
The South Africans managed to stake a claim to the playoff when Goosen, the winner of the U.S. Open in June, hit his approach to six feet at the 72nd hole and Els sank the putt for his second closing eagle in as many days.
They posted a 66 after the Danes had already made their way in with the day's best round of 7-under 65.
'We saw that Denmark made birdie on No. 18 and knew we needed an eagle,' said Els. 'Retief hit a beautiful 5-iron and I was able to make the putt to get us into the playoff.'
South Africa joined Australia and Spain as four-time winners of this event. Els also helped his country to its last World Cup victory when he partnered with Wayne Westner to win the title in 1996.
Defending champions Tiger Woods and David Duval, seeking a third straight Cup and the 24th overall for the U.S., played uninspired golf for the first half of the day but made a late surge to jump into contention during regulation.
Just when it seemed the American comeback would fall short, Woods chipped in for eagle at the 18th hole to make it a four-team logjam at 24-under-par 264.
But as quickly as the Americans entered the mix they found themselves fighting to stay in the playoff.
Woods drove way left off the tee at the par-5 18th, leaving Duval with no choice but to play his team's second shot from the trees out into the fairway. After Woods hit the third shot 30 feet left of the pin, Duval came up short with the putt for birdie.
It was a disappointing finish for the two top-ranked players in this week's 24-team field.
World No. 1 Woods helped start the U.S. rally by hitting his approach to three feet at the 15th to set up an easy Duval birdie. Duval, the reigning British Open champ and No. 3 in the world, responded with a shot to 12 feet at the next hole that Woods converted for birdie.
At the par-3 17th, Duval knocked his tee shot to 20 feet and Woods rolled in another putt to give the U.S. its third straight birdie.
Woods gave his partner a perfect drive at the 18th but Duval missed the green right with his 3-iron approach. With the pressure placed squarely on Woods' short game, the six-time major winner bumped his chip onto the edge of the green and the ball fed down to the hole then split the cup for a sensational eagle.
Woods' last minute heroics lifted the U.S. to a final-round 67.
New Zealand's Michael Campbell and David Smail, leaders by three shots heading into the final round, were tied for the lead on the final hole of regulation but couldn't take advantage of the 517-yard par-5.
Campbell pulled his second shot with a fairway wood left of the green then Smail's chip from a difficult lie stopped 20 short of the hole. The Kiwis needed the birdie putt to win but Campbell's attempt didn't reach the cup. Smail tapped in for par to give New Zealand a 2-under 70.
Like Woods, Smail drove poorly in the playoff and his tee shot came to rest in the right fairway bunker. Campbell then roped an iron out of the sand and watched his ball take a lucky bounce off the concrete lining of the water hazard in front of the green.
With the ball just off the putting surface, Smail hit his chip third shot fat and Campbell wound up missing the 12-foot birdie bid that remained, knocking New Zealand out of the playoff.
England's Paul Casey and Ian Poulter shot 67 to finish alone in fifth place at 21-under 267, three shots out of the playoff.
The Canadian tandem of Ian Leggatt and Tour Championship winner Mike Weir carded a 67 to tie for sixth at 20-under with Spain's Sergio Garcia and Miguel Angel Jimenez, who combined for a three-under 69.
Fiji, Argentina and France were together at 19-under, while Shigeki Maruyama and Toshi Izawa of host Japan finished alongside Scotland and Wales at minus-18.
Sunday's victory capped an incredible year for Goosen, who survived an 18-hole playoff to win his first major championship at the U.S. Open then added two European Tour titles to finish first on that circuit's Order of Merit.
The victory may also do wonders for Els, who is coming off a season in which he failed to win on the PGA Tour for the first time since 1993.
'Retief's had an unbelievable year and I think some of his good play has rubbed off on me finally,' said Els, who captured the first of his two U.S. Opens in a playoff in 1994. 'It's great to win.'
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