Colin Montgomerie, despite a great display of skill, and even greater guts, yesterday succumbed to Tiger Woods. But it took three play-off holes in the Deutsche Bank SAP Open for the world number one to maul his man into submission after the Scot had courageously defied the pain of an aching back.

Montgomerie, the overnight leader by one, had a final round of 69, three under par, to tie on 268 with Woods, who was round in 68. Justin Rose, with a creditable 67, was third, one shot behind. Woods won €450,000 to go with his $2m appearance fee, while Montgomerie made €300,000 and moved up to sixth place in the Volvo Order of Merit. Rose took away £169,000 to move into 16th spot.

Woods and Montgomerie were to play the 18th hole three times, halving it in par figures on the first two occasions before Montgomerie made a fatal mistake. He found a fairway bunker off the tee and, in attempting to reach the green, dumped his ball in the lake that runs along the right of the hole. After that a double-bogey six was inevitable and it left the way clear for Woods to retain his title.

Afterwards Montgomerie admitted that when warming up on the range he thought he would have to pull out. "It was very close. I felt I couldn't play. In the circumstances I am very proud of shooting a 69. In the play-off my back was getting far too sore, but at the end of the day the best man won."

Asked why the Scot had not won a major championship, Woods said: "He's a great champion whether he wins a major or not."

Given that Woods is capable of anything at any time it was clearly important for Montgomerie, one ahead overnight, to get some insurance against eventualities in the shape of early birdies. And he could hardly have done better, starting with three in succession.

The first and third are reachable par fives - both were on in two - but at the first Woods missed from four feet to only par the hole. He stood for ages in the address position, a trait that was to re-occur frequently thereafter.

But at the third he rammed in a 21-footer for an eagle, taking him to within two shots of Montgomerie, who merely birdied, and Woods got closer at the short fourth, where Montgomerie bunkered his tee shot and, with a relatively simple recovery facing him, played it poorly on to a grassy bank in front of him.

It saw Montgomerie on 19 under, one ahead of Woods, and at the fifth Woods had his chance to draw level.

Montgomerie missed a birdie putt of 10 feet with Woods only six feet away - but the world number one missed. The sharp intake of breath that accompanied the ball as it ran round the hole was evidence of the belief that he seldom misses that kind of chance.

He wearily retrieved the ball from the cup and he was no happier with his second to the eighth. It only just made the green and Woods spun angrily on his heels and lobbed the offending club at his bag. It was a mistake made worse by the fact that Montgomerie had made a similar error moments earlier.

They reached the turn with Montgomerie still one ahead, but Woods levelled at the 10th. Once again the American stood over the ball for ages, but this time he holed from10 feet.

Now the battle was really joined, head to head and level pegging, and it was Montgomerie who blinked first. The short 13th presents no particular problem for this class of player, but the Scot three-putted to fall behind for the first time.

But just when it seemed that Woods was likely to ease home, as he so often does, Montgomerie holed from 11 feet at the 15th for a birdie and they were level again at 20 under.

The 18th was pure drama. Woods missed the green, finishing on the first cut, and then Montgomerie flew the putting surface, ending up in thick grass at the back. Woods chipped poorly and ran eight feet past; Montgomerie chipped well to two feet for a certain par and then Woods, as he so often does, holed the putt when it really mattered.

Padraig Harrington had shot 70 to be nine shots off the pace set by Woods and Montgomerie, and Darren Clarke returned the same final round score - he had only three birdies all weekend - to finish a shot further back in a tie for 16th place.