The host side, trailing by seven points heading into Sunday's singles session, roared back into contention with a series of tight wins but the holders just did enough to cling on.
Shane Lowry delivered the crucial half-point in match number eight, taking Europe to 14 points by holing a putt to tie against Russell Henley.
Lowry had trailed by one heading to the 18th but a superb second shot allowed him to hole for birdie three after Henley had been forced to settle for a four.
That took the score to 14-11 and ensured Europe could not be beaten with three matches still out on the course.
That the contest got so close was remarkable given the size of Europe's lead, 11.5-4.5, after Saturday's play and how dispirited the Americans seemed.
Europe had needed to secure just two and a half points to retain the cup and the half came before play even started when Viktor Hovland withdrew injured and his clash with Harris English declared a draw.
But the hosts showed incredible fighting spirit to threaten the most unlikely of comebacks.
Cameron Young and Justin Thomas edged thrilling battles on the 18th green against big guns Justin Rose and Tommy Fleetwood and Xander Schauffele overpowered Jon Rahm 4&3.
Ludvig Aberg finally stemmed the tide as he beat Patrick Cantlay 2&1 and Matt Fitzpatrick held off a storming fightback from Bryson DeChambeau to halve his match having led by five after eight holes.
Yet the Americans continued to battle and Scottie Scheffler, after four defeats in the opening two days, saw off Rory McIlroy in a titantic struggle that also went to the 18th.
JJ Spaun delivered another point at the expense of Sepp Straka, but Lowry held his nerve when it mattered to fight back and claim his vital half.
Europe have captured the cup 13 out of 19 times since 1979, the start of the modern era, and have won five of the last 10 Ryder Cups on US soil.
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