Europe will have to complete another remarkable comeback on American soil if they are to win a fourth Ryder Cup in a row at Hazeltine National.
It was four years ago in Chicago that José María Olazábal's men recovered from a 10-6 deficit heading into the final day to win 14½-13½ and complete what became known as the Miracle at Medinah.
The odds will not be quite as highly stacked against Europe on Sunday but they will head into the 12 singles matches trailing 9½-6½ after losing Saturday afternoon's fourball session 3-1.
That still represents an excellent fightback after being whitewashed in the first session on Friday and with a combination of former winners and hungry rookies in his ranks, captain Darren Clarke still has a fighting chance of bringing the trophy home.
The fourth session started well with Rory McIlroy and Thomas Pieters winning their third point as a pair against Dustin Johnson and Brooks Koepka and at that moment, Europe were level in the contest at 6½-6½.
The Americans would go on to take the remaining three matches, however, with JB Holmes and Ryan Moore beating Lee Westwood and Danny Willett one up, Sergio Garcia and Martin Kaymer going down 2 and 1 to Matt Kuchar and Phil Mickelson, and Patrick Reed and Jordan Spieth beating Justin Rose and Henrik Stenson by the same score.
McIlroy and Pieters were playing in their third consecutive match after wins in the Friday fourballs and Saturday foursomes and McIlroy laid down a marker on the second as he holed a 35-footer to go one up.
Pieters then got on the drivable fifth in two for a brilliant eagle and an American bogey on the eighth followed by a McIlroy approach to tap-in range on the next had Europe four up at the turn.
Back-to-back Johnson birdies on the 11th and 12th cut the gap but Pieters holed from six and 12 feet on the next two to get to dormie four.
American birdies followed on the 15th and 16th but with McIlroy in the water, Pieters hit a lovely tee-shot to birdie the par-three 17th.
"It was incredible," said McIlroy. "I think just like yesterday in the fourball, we dovetailed really well all day.
"We both got off to a really good start. I sort of kept it going around the turn and then sort of disappeared for the last few holes and Thomas took over."
Pieters added: "I'm very happy I'm making a lot of putts, that's what's going to win you points and going to win matches. Hopefully I can continue that tomorrow."
Europe suffered late heartbreak in the second match as they fell behind for the first time on the 17th and saw Westwood miss a short putt to win the last.
Westwood, making his tenth Ryder Cup appearance this week, holed a 40-foot putt on the seventh to put Europe one up and another lengthy putt on the tenth eased them back ahead after a brilliant JB Holmes approach on the ninth.
Holmes produced more magic to level things on the 13th and two European bogeys on the 17th sent the Americans up the last with a lead.
"It's a shame," said Willett. "I think we both hit pretty good putts down the stretch. Obviously the last two, they are pretty tricky where the flag is and it's just a shame with two great golf shots in there to put the pressure on we couldn't capitalise.
"The job in hand is to try to win all 12 matches tomorrow. Looking at the score line, no one is at 14½, so there's a long way to go."
The United States were quickly two up in the third match after Garcia saw a putt agonisingly horseshoe on the third and then missed a short one on the fourth. A stunning approach to the seventh from the Spaniard cut the gap but Mickelson made a brilliant putt on the tenth before Garcia returned the favour on the 12th.
Back-to-back birdies on the 13th and 14th - the former after a huge Kuchar putt - then put the USA in control and while Garcia birdied the 16th, the Americans closed out.
"I felt like we both played great," said Garcia. "They played nicely but they didn't win it. We kind of gave it away a little bit with all the putts we missed. You know, it is what it is. You have to take those opportunities when you have them in match play and at The Ryder Cup and if you don't, then you struggle to try to win it."
Patrick Reed put in the performance of the week as he won six holes against Rose and Stenson.
A 25-foot birdie on the first from Stenson got Europe off to a great start but Reed birdied the fifth and then spun his approach to the sixth back into the cup for an eagle.
Back-to-back Reed birdies followed and while excellent putts from Stenson and Rose on the 12th and 13th offered a glimmer of hope, Reed rattled off two more birdies on the 14th and 15th.
A stunning holed bunker shot from Stenson on the 16th extended the contest but Europe could not make a gain on the next.
"He just played incredible golf, he was inspired," said Rose of Reed. "He punished us every time he had a wedge in his hands, he got it up-and-down.
"We didn't quite have it. I didn't have it this afternoon. It's tough playing four in a row, as they did as well. For Patrick to find that energy this afternoon is incredible.
"We're going to put out our line-up and we're going to look at each other man-to-man tomorrow. It's going to be eyeball to eyeball on the first tee, no partners, no friends out there on the golf course. Just go out and try to put a point on the board. That's everybody's mission."