MEDINAH, Ill. — Move over, Brookline, and make room for Medinah. There’s a new location that forever will be locked in Ryder Cup lore.

Turning the tables on a day from 13 years ago that still stings, Europe staged the greatest comeback — or benefited from the biggest collapse, depending on your perspective — in Ryder Cup history, pulling off a victory just as improbable as the one grabbed by the United States at The Country Club in 1999.

Just as emotional, too, at least to the Europeans, who sang and danced and hugged and sprayed champagne over their fans from a bridge near the clubhouse when it was over. Keeping former Ryder Cup icon Seve Ballesteros close to their hearts all week — and wearing his image on their sleeves Sunday — the Euros would have made the late Spaniard proud, somehow finding a way to win when the situation 24 hours earlier seemed hopelessly lost.

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But then, a slight glimmer, winning the last two matches in the Saturday twilight and taking the momentum into the evening, even though the United States held a 10-6 lead and had won or tied all four team sessions.

Come Sunday, the side known to embrace the team concept in these biennial matches split up as 12 individuals, then went out and played as one, winning early, battling in the middle, and rallying late. It added up to the closest possible victory at the 39th Ryder Cup, 14½-13½, the second straight time Europe has won by that score and the fourth time since 1995, showcasing how razor thin and dramatic the competition has become.

This one wasn’t decided until Martin Kaymer holed a 6-foot par putt on the 18th hole in the next-to-last match, beating Steve Stricker, 1 up, and giving Europe its 14th point, guaranteeing it would be bringing the trophy home with no worse than a tie. They did so with a win minutes later, when Tiger Woods (winless on the week) missed a short par putt and conceded a similar-length try to Francesco Molinari, providing the Euros one more half-point and leaving the Americans to wonder what happened.

“It’s going down in history. We talk about Brookline in ’99, losing that one. We wanted to come back and show that we could win from behind, too,” said Luke Donald, who beat Bubba Watson in the first singles match, 2 and 1. “We wanted to do it for Seve. We wanted to show our grit.”

Plenty of that was shown, at least by the Europeans, who won eight of the 12 singles matches and halved the last one. Captain Jose Maria Olazabal, sensing an opening with the late Saturday rally, knew he needed to capitalize, and sent out his big guns early: Donald, Ian Poulter, Rory McIlroy, Justin Rose.

All four won their matches, none more impressively than Rose, who holed a long par putt on No. 16 to remain one down to Phil Mickelson, drained a 35-footer for birdie at No. 17 to square the match, then dropped a 15-footer at the 18th to win it, 1 up.

“Those are the three biggest putts I’ve ever made in my career under pressure,” Rose said. “The Ryder Cup is as big as it gets.”

Especially when a match gets to the 18th hole. It happened 13 times at Medinah, and only once did the Americans win the hole: Jason Dufner won the 18th with a par Sunday, beating Peter Hanson, 2 up. Five times the Europeans won No. 18, including four times in singles. In addition to Rose, Poulter, Sergio Garcia, and Molinari also won No. 18.

Garcia’s point was pivotal. Like Rose, he trailed by one hole late in his match against Jim Furyk. But Furyk, as has been his habit this year, couldn’t close: A bogey on No. 17 to lose the lead, another bogey at No. 18 to lose the match. What had been a point that Love was counting on went the other way. Furyk, a captain’s pick, lost two matches that went the distance.

“It’s the lowest point of my year,” said Furyk, who also had chances to win the US Open and Bridgestone Invitational, losing both late. “But I’ve got 11 guys, I’ve got a captain, I’ve got four assistants that I know will pat me on the back, that know how I feel, understand how I feel.”

Stricker, also a captain’s pick, was 0-4 on the week, and three-putted No. 17 to fall a hole behind Kaymer, setting up a sobering thought for the Americans: If Stricker didn’t win the 18th, the US couldn’t win. And when Kaymer knocked in his 6-footer, the teams’ fates were sealed.

“It’s a feeling that I’ve never had before,” said Kaymer, who lost his only team match. “Now I know how it really feels to win the Ryder Cup.”

Kaymer said he spent time on Friday talking with Bernhard Langer, the German who also faced a 6-foot par putt to win the Ryder Cup. He missed that attempt in 1991, giving the US a 1-point win at Kiawah Island.

This time it was different, in so many ways.

Olazabal closed his eyes when Kaymer putted for the win, and when the crowd’s reaction gave him the result, he opened them, tears visible. A two-year journey finally complete, Olazabal, a two-time major champion who played on seven European Ryder Cup teams, has something else to be known for now. He was on that ’99 team at The Country Club, and was on the 17th green when the US celebrated Justin Leonard’s famous cup-clinching putt.

On Saturday night, his message to his team was blunt, and brief. Believe.

“I think the boys understood that believing was the most important thing,” Olazabal said. “We started to make a few putts, the Americans started to miss them. This one is for Europe.”