Needing to claim eight points in the concluding singles to retain the trophy, Europe won six of the first eight encounters before Germany's Martin Kaymer secured the vital point to retain the Cup by beating Steve Stricker one up.
After Stricker had coolly holed his par putt from eight feet at the last, Kaymer buried his five-footer for a matching par before thrusting his arms skywards in delight as European fans erupted with deafening cheers at Medinah Country Club.
"It's undescribable," the German told reporters after being swamped by his jubilant team mates as roars of "Ole, Ole, Ole" echoed across Medinah. "I was so nervous the last two, three holes. I loved it. It's amazing."
With the chance of a tie resting on the final match, Tiger Woods astonishingly missed a three-foot par putt on the 18th green to halve his contest with Italy's Francesco Molinari, handing Europe outright victory.
Europe, who sent out their best players early, emulated the miracle comeback achieved by the U.S. at Brookline in 1999 when they also overhauled a deficit of 10-6 on the final day.
"We believed in our hearts we could win this," said Englishman Luke Donald, who earned Europe's first point of the day in the opening match with a 2&1 win over Masters champion Bubba Watson. "It's been done before and we believed we could turn it around."
The Europeans drew inspiration on Sunday from their beloved Ballesteros, who died last year aged 54 after a battle with cancer, with every player wearing the navy blue colours favoured by the Spaniard in the final rounds of tournaments.
"Seve will always be present with this team," said a teary-eyed Olazabal, for whom his compatriot Ballesteros was both a friend and mentor. "He was a big factor for this event, for the European side.
"Last night when we were having that (team) meeting, I think the boys understood that believing was the most important thing, and I think they did. This one is for the whole of Europe."
U.S. captain Davis Love III, whose team been in a dominant position overnight when leading 10-6, was stunned by the defeat.
"We know what it feels like now from the '99 Ryder Cup. It's a little bit shocking. We were playing so well, everyone on our team was playing so well," he said.
"I wouldn't have done anything different. They played great. We had a couple matches get flipped there at the end that made it a little bit easier on them."
Donald set the tone for a remarkable day for European golf, fending off a late fightback by Watson before ending their match on the 17th green.
"I had a lot of responsibility going out number 1 to get some blue up on the board early," Donald said. "Bubba put some pressure on me at the end, and I was glad I held on."
Scot Paul Lawrie, competing in the Cup for the first time since 1999, crushed Brandt Snedeker 5&3 before Northern Irish world number one Rory McIlroy beat Keegan Bradley 2&1.
McIlroy gave his team an early scare after making his teeoff by barely 10 minutes due to a mix-up over his starting time.
Englishman Ian Poulter never led in his match until he won the par-three 17th with a par before beating U.S. Open champion Webb Simpson two up after conjuring a miraculous birdie from trees at the last.
The first U.S. point came when long-hitting Dustin Johnson beat Belgian Cup rookie Nicolas Colsaerts 3&2 but England's Justin Rose then came from one down to Phil Mickelson after 16 holes to win one up with a birdie-birdie finish.
Rose drained a 35-footer at the tricky par-three 17th to square the match, then coolly sank a 12-footer at the 18th after Mickelson had over-hit the green with his approach.
"The Ryder Cup is as big as it gets, and to play Phil ... he always seems to bring out the best in me," said Rose, who also beat Mickelson in the singles at Valhalla in 2008.
Though Zach Johnson and Cup rookie Jason Dufner added further points for the U.S. after never trailing in their matches against Northern Ireland's Graeme McDowell (2&1) and Swede Peter Hanson (two up), the late momentum went Europe's way.
Woods and Stricker, who had been beaten in their three matches together earlier in the week, both had to win their singles encounters to ensure a U.S. Cup victory but both fell short.
