The American pair were five over par for the first three holes as they crumbled to a 9&7 defeat by Viktor Hovland and Ludvig Aberg, the largest margin of victory in any 18-hole match in the event’s history.
Scheffler was pictured fighting back tears and being comforted by his wife Meredith as the enormity of the loss sank in, the previous biggest margin being 7&6.
The PA news agency understands Scheffler was keen to be given the chance to make amends in the afternoon fourballs, but was left out by US captain Zach Johnson.
The only bright spot of the morning session for the visitors came when Max Homa and Brian Harman secured a first win of the contest, the former chipping in for an eagle on the 16th to see off Shane Lowry and Sepp Straka 4&2.
However, moments later Rory McIlroy and Tommy Fleetwood completed a hard-fought victory over Justin Thomas and Jordan Spieth, the Northern Irishman holing the winning putt from 12 feet on the 17th to secure his third point.
“Last night we talked about enjoying what we did yesterday but coming out and showing no mercy today and the way Ludvig and Viktor started off set the tone,” McIlroy said.
“I’m delighted to get another point on the board for Europe.”
Jon Rahm and Tyrrell Hatton also had to work hard to secure their second victory together when they lost three holes in a row to Patrick Cantlay and Xander Schauffele to be pegged back to all square.
However, Hatton’s birdie putt on the 16th edged them in front again and Rahm then came agonisingly close to making a hole-in-one on the 17th.
Cantlay responded with an excellent tee shot of his own, but Schauffele’s birdie attempt from three feet caught the edge of the hole and span out.
That made the overall score 9.5 to 2.5 and meant Europe needed just five points from the remaining 16 for victory.
Europe captain Luke Donald had warned his side to be wary of the US players reacting like “a wounded animal” as they looked to overturn a record-equalling five-point deficit, but the only wounds on show from Scheffler and Koepka were entirely self-inflicted.
Hovland and Aberg were one over par for the first three holes but won them all, the Americans making a double bogey on the first, a bogey on the second and another double bogey on the third.
Aberg was then inches away from a hole-in-one on the fourth, another birdie on the sixth took the European pair five up and with both American players struggling badly it was only a matter of time before they were put out of their misery.
Hovland was full of praise for his partner, who only turned professional in June and was given a wild card after winning the final qualifying event.
“He’s a stud,” Hovland said. “He doesn’t miss a shot, so it’s easy when I’m playing well and he’s playing well and we are just feeding off each other.”