Woods finished second with five skins and $310,000. Adam Scott, the only player to win anything on Saturday with two skins and $50,000 on the second hole, took third. Annika Sorenstam, who won five skins last year, was shut out in 2004.
Scott and Sorenstam were eliminated on the first playoff hole, so it came down to Couples, the all-time leader in skins and money, and Woods, who has never won this event.
At the par-three 17th, the fourth extra hole, Woods' tee ball landed in the water left of the green. Couples, the 1992 Masters champion, played safely over the flag, some 25 feet from the hole. He got down in two to win the final three skins and $340,000.
'This is a lot of fun,' said Couples, who defeated Masters champion Phil Mickelson in a four-hole playoff last year as well. 'I felt like I played with him all day. I'm 45 and I hope to keep going.'
Couples and Woods halved the first playoff hole, but Woods looked to be in great shape at the second extra hole, the 17th. He had 10 feet for birdie, but missed left.
The third playoff hole was the par-five 18th, and Woods had 15 feet for birdie. Woods' birdie putt came up short, then Couples missed a 12-foot chance left of the hole that would have won.
Then Couples cooly lagged his birdie try down the hill to tap-in range at 17.
Couples started Sunday's second nine strongly. The last seven skins on Saturday were carried over to the 10th hole on Sunday. Couples ran home a 25- foot birdie putt to win the eight skins and $300,000.
'Downwind, I figured there would be a birdie here,' admitted Couples, who now has 77 skins and $3,515,000 in 11 appearances. 'I got a great line from Annika's chip and happened to make it. I feel very fortunate.'
The quartet carried the next five skins over until the par-four 15th. Woods had the best look at birdie and converted. He hit a knock-down six-iron in the windy conditions and drained the six-footer to win five skins and $310,000. That eclipsed the total money he won in the four prior Skins Game by $85,000.
'It was nice getting off the bagel there,' said Woods after his birdie at 15.
Woods, who won a car for a fan by being closest to the pin at 17, thought he had a birdie in regulation, but his putt died at the end, meaning 18, which was worth $200,000.
No player won the 18th, so that meant that only four holes were won, the fewest in tournament history.
Final Results (skins won):
Couples - $640,000 (11)
Woods - $310,000 (5)
Scott - $50,000 (2)
Sorenstam - $0