The £432,000 (€557,163) first prize takes the Swede ahead of double major winner Padraig Harrington in the Order of Merit with just four events of the season remaining.

Karlsson, who won the Mercedes-Benz Championship in Germany the week before the Ryder Cup, plans to play one more event before the season-ending Volvo Masters but Harrington will only compete at Valderrama.

But even if he goes on to win the Harry Vardon Trophy for the first time, Karlsson concedes Harrington’s victories this year in the Open Championship and USPGA Championship mean he will be the true European number one.

“I still rate Padraig’s year higher than mine,” admitted Karlsson. “If you’ve won two majors there’s no doubt who is the best player this year.”

Until his victory in Cologne, Karlsson had gone two years without a victory but qualified for his second Ryder Cup on the back of nine top-10 finishes this season – including eighth in the US Masters, fourth in the US Open and seventh in the Open.

“I felt at ease today after getting that win under my belt and felt very comfortable going out there in the play-off,” said the 39-year-old.

“I’ve birdied that hole three times in a row now and I just fancied my chances when I got that yardage.

“It’s a relaxing event and you just want to go out there and have fun and enjoy it, although I wouldn’t have said that yesterday. I was a bad boy a couple of times during my 76 at Carnoustie!”

On a day of low scoring in benign conditions on the Old Course, Karlsson and Fisher set the clubhouse target after matching rounds of 65.

Kaymer held a one-shot lead on the 17th tee but bogeyed the famous Road Hole after coming up short of the green, and then missed a birdie putt for the title from eight feet on the 18th.

The 23-year-old German then also missed from 12ft for birdie on the first extra hole – after Fisher’s hopes disappeared when he drove into the Swilcan Burn - but Karlsson made no mistake after a superb approach to three feet.

“It’s disappointing, especially after having chances on the last two holes to win, but overall it was a really good week for me,” said Kaymer, who has won twice this season, including on home soil just two weeks after his mother died of cancer.

“It has been a very special week to play with my brother and father in the team event.”

Harrington began the day just two off the lead but could only manage a closing 71 and again pointed to fatigue as the reason behind his sub-par recent performances.

The 37-year-old, who won just half a point for the second Ryder Cup in succession at Valhalla, said: “It’s hard to get away with it on a Sunday when you are not prepared right. I know myself I’m not on top of my game.

“I’ll have a battle on my hands for the Order of Merit for sure. It’s in Robert’s hands now.”