Inspired once again by the all-conquering pairing of Keegan Bradley and Phil Mickelson, Davis Love III's team won three of the four morning foursomes and looked like repeating the trick in the afternoon's fourballs.
But dramatic late points from Luke Donald and Sergio Garcia, Rory McIlroy and the brilliant Ian Poulter - his third of the competition - gave Europe late hope of an unlikely comeback.
"That was unbelievable," said Poulter, who notched up his 11th victory in 14 matches, despite being two down with six holes to play.
"We had to get something going. From then on my putter warmed up nicely, having been pretty cold for the first 13 holes.
"Then it just went crazy. It was tough out there. We're in Chicago, they've had a few drinks today and they weren't making it easy for us. I will be honest, it was brutal."
Since the competition expanded to include mainland Europe in 1979, the biggest comeback on the final day of singles came at Brookline in 1999, when the US overhauled a 10-6 deficit on the Sunday to win by a single point.The hosts were consistently superior on the slippery, sloping Medinah greens, nailing clutch putts as Europe's players struggled to read the fast lines.
If that is a chastening statistic for the visitors' captain Jose Maria Olazabal, he knows his side will have no chance at all unless there is a dramatic reversal of form from the first two days.
The gap between the two sides has at times been immense, not only on the overall scoreboard but in too many individual matches.
In a horribly one-sided morning session, Mickelson and Bradley had equalled the biggest foursomes win in Ryder Cup history as the US roared out to an 8-4 lead.
The American pairing had won both their foursomes and fourballs matches on Friday and were even more dominant in a crushing 7&6 win over Luke Donald and Lee Westwood.
Their margin was almost matched in the afternoon by Bubba Watson and Webb Simpson's 5&4 butchering of Justin Rose and Francesco Molinari.
Watson has been one of the darlings of the pumped-up Medinah crowd, and his huge driving on a course with almost no rough, allied to Simpson's vastly improved putting, was a matchless combination.
Dustin Johnson drained a 30-footer on the 17th green to establish a late winning lead for his pairing with Matt Kuchar over Paul Lawrie and Nicolas Colsaerts as Europe came close to capitulation.
In a see-saw match, the Belgian rookie Colsaerts almost holed his approach to rescue a half on the 18th.
But as so often on a frustrating afternoon the European ball flirted with the hole yet refused to drop, and when Colsaerts could only run the resulting 15-foot putt past the right edge, the American pair had the point.
Garcia and Donald had been four-up on Woods and Stricker at the turn, only for a previously out-of-touch Woods to find his touch on the back nine and embark on a birdie blitz.
A nerveless eight-foot putt from Donald on the 15th restored a two-hole advantage with three to play before Woods conjured up yet another birdie on 16 to leave Europe just one up.
But it was the miraculous late charge of Poulter that kept alive European hopes, five birdies on the bounce clawing back a two-hole deficit on Jason Dufner and Zach Johnson before nerveless putting on the 17th and 18th secured the precious point.After brilliant tee-shots from both Woods and Donald on the 17th the match came down to a Stricker putt on the 18th, and he could only lip out from eight feet to send his pairing to their third defeat in three.
Earlier in the day, Dufner and Johnson had beaten Garcia and Colsaerts 2&1 while Jim Furyk and Brandt Snedeker saw off Graeme McDowell and McIlroy.
Europe's solitary point of the morning was won by the fired-up Poulter and Rose, who survived a seven-foot Simpson birdie attempt on the 18th to hang on one up.
The Englishmen won three holes out of four from the ninth to go two up after 12, an advantage they maintained until the 16th when Rose missed a five-foot putt to allow the Americans to win with a bogey.
Rose atoned for that miss with a terrific 40-foot putt on the last, which was conceded, but Simpson still had a 10-foot putt to win the hole and halve the match only to slide it by.
McIlroy and McDowell's match was a repeat of Friday morning's foursomes, and as then it went down to the last hole.
The Northern Irish duo failed to sink a single birdie putt until McIlroy's effort on the 16th - their four on the par-five 14th had been conceded - reduced their deficit to one down.
However, the world number one missed a 10-foot putt to win the 17th and level the match.
On the par-four 18th, Furyk kept his nerve to find the green with his second shot while McDowell's approach landed in the greenside rough. McIlroy's chip drifted past the hole and when Snedeker rolled his putt to within a foot, Europe conceded to lose the match by one hole.
In the other match, Colsaerts struggled to find the form he showed on Friday afternoon when he rolled in eight birdies and an eagle.
The Belgian did sink a birdie putt from 12 feet on the 11th to level his and Garcia's match but he then missed from two feet on the 13th as they fell two holes down.
Overnight, Olazabal had delivered a stinging pep-talk to his team. But once again it was the home side who snatched the early initiative and an advantage that should prove decisive.
Europe's golfers must produce a historic turnaround in Sunday's singles if they are to retain the Ryder Cup after another day of American domination.
USA 10-6 Europe
Watson/Simpson lost to Rose/Poulter 1 up
Bradley/Mickelson beat Donald/Westwood 7&6
Dufner/Johnson beat Colsaerts/Garcia 2&1
Furyk/Snedeker beat McIlroy/McDowell 1 up
Watson/Simpson beat Rose/Molinari 5&4
Johnson/Kuchar beat Colsaerts/Lawrie 1 up
Woods/Stricker lost to Garcia/Donald 1 up
Dufner/Johnson lost to McIlroy/Poulter 1 up