MEDINAH, Ill. — Erasing some of their worst Ryder Cup memories, the Europeans wore the image of Seve Ballesteros on their sleeves and played their hearts out Sunday at Medinah to match the greatest comeback in history and head home with that precious gold trophy.

Europe got its payback for Brookline. Martin Kaymer gave German golf redemption for Kiawah Island.

Jose Maria Olazabal squeezed his eyes and fought back tears when Kaymer holed a 6-foot par putt — about the same length that countryman Bernhard Langer missed at Kiawah in 1991 — to beat Steve Stricker and give Europe the point it needed to keep the cup.

Tiger Woods missed a 3½-foot par putt on the 18th hole and conceded a par to Francesco Molinari that halved their match, that extra half-point making it a clear-cut win for Europe, 14½-13½.

Woods and Stricker, the anchors in the lineup, didn't win a single match at Medinah.

"This one is for all of Europe," Olazabal said. "Seve will always be present with this team. He was a big factor for this event for the European side, and last night when we were having that meeting, I think the boys understood that believing was the most important thing. And I think they did."

Ian Poulter was the first to embrace Olazabal, which was only fitting.

It was Poulter who gave Europe hope Saturday evening when he made five straight birdies to turn a loss into a win and swing momentum in Europe's favor. Poulter was up to his fist-pumping, eye-bulging tricks again on the final day, winning the last two holes in his match against U.S. Open champion Webb Simpson.

And he had plenty of help. Europe's top five players in the lineup all won, including Rory McIlroy, who was lucky to be playing. McIlroy kept thinking his match was at 12:25 p.m. — it was listed in Eastern time, not Central — and he needed a police escort to get to the course with 10 minutes to spare. Then, he came up with key birdies to hand Keegan Bradley his first loss of the week.

The biggest match might have belonged to Justin Rose. He was on the verge of losing to Phil Mickelson when Rose holed a 12-foot par putt to halve the 16th, made a 35-foot birdie putt from the back of the 17th green to win the hole, and then closed out Mickelson with a 12-foot birdie on the last hole.

Six of the 12 matches went to the 18th hole on Sunday. The Americans won only one of them.

The Americans also rallied from a four-point deficit to win in 1999 at Brookline. This was different, though. The Americans won big in those early matches. At Medinah, so many of them could have gone either way.

It was so close, so tense, that either side could have won the Ryder Cup down to the very end.

Stricker made an 8-foot par putt on the 18th, and Kaymer faced a par putt from 6 feet to win the match. If he missed, the Americans would get a half-point, and Woods was leading 1-up over Molinari and in the middle of the 18th fairway.

Kaymer, a former No. 1 and major champion who has struggled all year, poured it in the middle and the celebration was on.

"It's a feeling I never had before," Kaymer said. "On Friday, I sat down with Bernhard and talked a little bit about the Ryder Cup because my attitude was not the right one. But now I know how important the Ryder Cup is."

He could barely speak at this point, not so much from pure emotion but having to scream over the crowd behind him. Players were hugging and crying, and the small European contingent that had been drowned out all week was serenading themselves with what has become the theme song of the Ryder Cup.

"Ole, ole, ole, ole," they sang merrily, even as the teams prepared for the closing ceremony.

Europe now has won seven of the last nine Ryder Cups, and even more remarkable about this comeback is that they did it on the road.