Given a chance to win, he wasn't about to waste it.
It came on the 10th anniversary of his turning pro, and it gave Woods his 52nd career victory to match Byron Nelson for fifth all time.
"Just end this thing now," Woods said he told himself on the birdie putt at No. 17. "If I make mine, it's over."
For complete coverage, go to FOXSports.com.
And it was, but not before a roller-coaster round that capped off a strange week.
Woods ended his round Friday by hitting a 9-iron over the green, onto the clubhouse roof and down the other side. He followed that by making four straight bogeys Saturday, his longest such streak in nearly 10 years.
Under darkening clouds in the final round, he went from a two-shot deficit to a three-shot lead in a span of four holes, then lost a three-shot lead over the final three holes to slip into a playoff.
"I was very lucky to even be in the playoff," Woods said.
The result was familiar, especially at this event. Woods now has won five times at Firestone, the most of any golf course on the PGA Tour. He has won four times each at Augusta National and Torrey Pines.
His latest winning streak required more than a little luck. Woods has won his last four starts, his longest winning streak since he won six in a row at the end of the 1999 season and the beginning of 2000.
That was Woods at his peak, and he might be heading there again. He doesn't always win easily, but he finds a way.
"You don't know how many chances you're going to have to beat Tiger in a playoff in your career," Cink said.
Cink, who missed an 8-foot par putt that would have won on the third playoff hole, hit into the bunker and blasted out to 6 feet on the 17th. Before he could save par, he wound up shaking hands with Woods and watching him collect another World Golf Championship.
"I didn't convert, and he did," Cink said. "That's why he has the trophy."
And to think it was 10 years ago Sunday — Aug. 27, 1996 — that he introduced himself to the PGA Tour by saying, "Hello, world."
These days, he is saying "goodbye" to the competition.
A week ago, he captured the PGA Championship for his 12th career major, trailing only the 18 won by Jack Nicklaus. He now has 52 victories, and only Arnold Palmer (62), Ben Hogan (64), Nicklaus (73) and Sam Snead (82) have more.
Even so, Woods said he is only worried about himself.
"It's always yourself," he said. "You're always trying to better what you've done in the past — always. Hopefully, that's good enough to beat the rest of the guys."
Cink was looking for a peculiar repeat.
Two years ago, he validated Hal Sutton's decision to make him a captain's pick for the Ryder Cup by winning at Firestone. Tom Lehman picked him on Monday, and Cink nearly delivered his first victory in two years.
"There were a lot of highs and lows today," Cink said. "Unfortunately, I finished on a low."
Cink had a shot to win on the first three playoff holes — a 20-foot chip that grazed the lip at No. 18, an 18-foot putt that missed on the high side at No. 17, and an 8-foot par putt on the 18th again that missed to the right.
Woods was in trouble most of the time. On the first extra hole, he pulled his approach long and left into the rough, but pitched beautifully to 5 feet and escaped with par. The second time playing the 18th in the playoff, Woods found a greenside bunker 40 feet from the flag, blasted out to 8 feet and left it inches short.
Victory seemed inevitable for Woods, as it often does at Firestone, when he turned a two-shot deficit at the turn into a three-shot lead with his 20-foot birdie on the 13th. No one else was making birdies, and Woods wasn't making mistakes.
That changed on the 652-yard 16th hole, when Woods hit into the trees down the right side and had to pitch out to the fairway, leaving himself some 230 yards to the flag. He went over the green, chipped to 4 feet and missed the par putt.
Cink, who started the final round with a one-shot lead, holed a 15-foot birdie on the 16th hole, then made a 20-foot birdie putt on the 17th hole to tie Woods atop the leaderboard.
Woods (68) and Cink (69) each had to make a testy 3-footer for par on the 18th hole in regulation — Woods after leaving his 20-foot putt from the fringe short, Cink after lagging from 90 feet at the front of the green.
Jim Furyk closed with a 68 to finish one shot behind, making a 10-foot par save on the 18th to give himself a chance. Paul Casey of England, among four players atop the leaderboard at one point in the final round, stumbled on the back nine and shot 71. He tied for fourth along with Angel Cabrera (65), Lucas Glover (69) and Davis Love III (71).
Woods, Cink and Furyk headed to the Cleveland airport to join the rest of their U.S. Ryder Cup team for a charter flight to Ireland, where they plan to spend the next two days practicing at The K Club.
Woods and Phil Mickelson, the top two players in the world, rearranged their schedule to make the trip. Asked if that sent a strong message to their 10 teammates, captain Tom Lehman replied, "It sends a strong message to the other team."
When the Americans return on Wednesday, Woods will go for a fifth straight victory when he plays the Deutsche Bank Championship outside Boston. He already has won six of his 13 starts on the PGA Tour this year.
For complete coverage, go to FOXSports.com.