This was Woods’s fourth win in succession — following victories at the Open Championship, the Buick Open and the US PGA Championship — and his fifth in a tournament dubbed “Tiger’s Benefit” for the $6.6 million (about £3.5 million) he has milked from the event in the past eight years.

Woods, who was taken to the seventh extra hole by Jim Furyk here at the Firestone Country Club in 2001, has now won 13 out of 15 play-offs in his ten-year professional career. But he was forced to work particularly hard by Cink and would have lost had his Ryder Cup colleague sunk an eight-foot putt for par at the third extra hole, the 18th.

Rarely do you get a second chance against the world No 1, however, and it seemed almost inevitable that Woods would go on to win.

Playing the 17th for the second time, Woods hit an eight-iron 166 yards to within eight feet of the hole and wrapped up victory with a birdie three after Cink had found a greenside bunker with his second shot.

It had been a long day for Woods, who had looked finally to be succumbing to fatigue. “I was not hitting it at all well the last two days,” Woods said. “I was just trying to piece it together somehow to keep myself in the ballgame.”

Which is exactly what he did. Like all great champions, Woods has perfected the art of winning ugly and all of those around him knew they could take nothing for granted.

At one point, it looked as if Casey might finally come through for the biggest victory of his career. He reached the turn in 33, with birdies at the 3rd and 8th and led Woods, who went out in 35, by two and Cink by one.

But as has happened so many times before, the opposition started melting away when Woods began to apply a little heat. With putts of 10, 35 and 22 feet, he picked up three birdies in four holes from the 10th, while Casey was dropping shots at the 11th and 13th. Two shots back after nine was transformed into three shots ahead with five to play.

At that point, the game would normally be over. Cink had played erratically all day and made a series of scrambled pars on the front nine.

But when Woods bogeyed the 16th following another wayward tee shot and Cink birdied that hole and the 17th, they were level on ten under par — which is where they stayed.

Casey, who had a round of 71, for a total of 273, finished tied fourth in the end and, with the $246,000 winnings, is closing in on David Howell at the top of the European Order of Merit. “I’m very happy with that,” Casey said. “I love playing here and my record isn’t too bad. It was the first time playing in the final group with Tiger, so that was an experience, too.”

José María Olazábal forced his way to fifth in the Ryder Cup standings after finishing tied for 22nd, but is not yet guaranteed his place against the United States at the K Club next month. That will depend on what happens at the BMW Open this week in Munich.

Lee Westwood, who pulled out with flu, and Ian Poulter, who was thirteenth, can’t qualify automatically and will be reliant on wild-card picks from Ian Woosnam, the captain. Donald finished on six under par, in a share of eighth place.

FINAL SCORES

United States unless stated

270 T Woods 67, 64, 71, 68; S Cink 70, 67, 64, 69 (Woods won at hole 17 in a play-off)

271: J Furyk 69, 65, 69, 68

273 A Cabrera (Arg) 70, 68, 70, 65; D Love III 67, 65, 70, 71; L Glover 66, 69, 69, 69; P Casey (Eng) 69, 69, 64, 71

274: L Donald (Eng) 67, 69, 70, 68; D Toms 67, 74, 65, 68

275: A Oberholser 70, 71, 69, 65; JJ Henry 70, 68, 68, 69; A Scott (Aus) 63, 71, 71, 70

277: I Poulter (Eng) 71, 71, 67, 68; T Immelman (SA) 69, 70, 68, 70; K Stadler 68, 67, 70, 72

278: B Crane 73, 67, 70, 68

279: M Campbell (Aus) 67, 71, 70, 71

280: S Ames (Can) 69, 70, 71, 70; V Taylor 71, 67, 71, 71; R Gamez 70, 67, 72, 71; T Bjorn (Den) 72, 67, 67, 74

281: J M Olazábal (Sp) 68, 70, 74, 69; K J Choi (S Kor) 75, 70, 67, 69; R Allenby (Aus) 71, 71, 68, 71; S García (Sp) 69, 73, 68, 71; M Weir (Can) 69, 71, 69, 72

282: P Harrington (Ire) 73, 71, 70, 68; C Di Marco 68, 72, 71, 71; C Pettersson (Swe) 70, 72, 68, 72; K Perry 73, 70, 66, 73

283: B Faxon 69, 69, 75, 70; N O'Hern (Aus) 72, 69, 71, 71; H Stenson (Swe) 75, 73, 67, 68; J Leonard 70, 69, 72, 72; E Els (SA) 68, 67, 70, 78