Trailing 6-2 overnight, Padraig Harrington’s team lost the opening six holes in the top two games in the second-day foursomes before rallying to lead the session at one point.
But, as had been the case on the opening morning at the Wisconsin venue, Europe’s sole point was delivered by Spanish duo Sergio Garcia and Jon Rahm.
One of those pairings to be three down heading to the fourth tee, they fought back brilliantly to beat Brooks Koepka and Daniel Berger 3&1.
The win, which came in a contest that saw Koepka swear at two officials over a rules issue, took Garcia’s all-time record points total to 27.5.
He is also now the outright holder of the record for most matches won, having edged ahead of Nick Faldo with 24.
But, in the closest of the sessions so far, the three other games all ended in victories for Steve Stricker’s side as they moved into a commanding 9-3 lead – their biggest cushion at this stage since 1975.
Sent out first for the second day running after an impressive win in the same format on Friday, Rahm and Garcia started slowly on this occasion and, as a consequence, couldn’t deliver the early blue on the board that Harrington would have been looking for.
Even worse, the Spaniards lost the opening three holes as Berger holed a five-footer for birdie at the first, the Americans then got home in two at the par-5 second before Garcia missed the green left at the short third.
Rahm’s lovely chip at the fourth got one back before the world No 1, having done exactly the same thing the previous morning, found water with Europe’s second shot at the par-5 fifth to lose that cheaply.
With Casey and Hatton also falling behind early on, the visitors badly needed the top pairing to light a spark and they provided that by getting back to all square by the turn.
Garcia almost holed their approach at the sixth then, after Berger had missed from four feet for a win at the next, he then knocked in a 15-footer at the eighth.
The event’s all-time record points scorer had the bit between his teeth and ‘Vamos’ was the cry as he chipped in from just short of the green at the ninth for a birdie-3.
Incredibly, the Spaniards then got their noses in front when a great tee shot from Rahm set up the opportunity for Garcia to convert from 10 feet for a birdie-2 at the 12th then won the next hole as well with a par.
It was back to one up after the 14th before it took around 15 minutes for a rules issue to be resolved and the Americans didn’t do themselves any favours in the process.
After Berger’s drive at the 15th had finished in a clump of grass at the edge of a bunker, Koepka called in a rules official asking for a free drop.
With Berger having an awful lot to say about it, that request was rejected but Koepka then asked for a second opinion only to get the same answer.
“If I break my wrist, it's on fucking both of you,” he said to the two officials, referring obviously to the fact he’d injured his wrist playing in a shot in the Tour Championship in Atlanta earlier in the month and being forced to withdraw.
Despite fearing that, the four-time major winner decided against taking a penalty drop and, after all the hooha, he hit a brilliant shot to find the green and walk off with a half.
It was vintage Garcia, though, when he then hit a majestic approach to set up a conceded eagle win for the Europeans at the 16th and one of the great comeback triumphs in the event’s history was clinched with a solid par at the short 17th.
“It means a lot,” admitted Rahm of the second point delivered by the Spaniards. “We woke up on six and played some unbelievable golf from then on.”
Dustin Johnson’s first-day performance had been the best from the highest-ranked American since Corey Pavin in 1995 and the world No 2 wasted no time hitting his stride once again.
He stiffed a chip at the first, showed a deft touch again around the greens to set up Open champion Collin Morikawa for a six-foot birdie at the second before then chipping in at the third for a 2.
Hatton had holed a testing birdie putt in the gathering gloom on Friday to secure a valuable half point in the fourballs, but the two-time Dunhill Links champion was out of sorts in this assignment and Casey wasn’t firing on all cylinders either.
As a result, they found themselves four down after eight and, though a Casey hole out for an eagle 2 at the 14th got the Europeans back to just one behind, they eventually lost that battle 2&1.
The all-rookie pairing of Viktor Hovald Hovland and Bernd Wiesberger got off to the perfect start by playing the opening hole best out of the Europeans as they won that with a straightforward birdie.
Buoyed by that start, they quickly went three up, a par proving good enough at the third and Wiesberger hitting their approach to around five feet at the sixth.
But, following a run of holes that saw both Thomas and Spieth find their putting touch as well as a long effort from Hovland incredibly staying above ground, that match also returned to where it had started.
Not for long as the Americans couldn’t get out of a greenside bunker at the 11th, failing to do so with two attempts, but a run of three winning holes for Spieth and Thomas was capped by a brilliant eagle-3 at the 16th as they went on to triumph by two holes.
Lee Westwood’s record-equalling 11th appearance continued to prove fruitless despite making a bright start alongside fellow Englishman Matt Fitzpatrick as they were paired again in the alternate shot format despite losing on day one.
Helped by a lovely wedge shot from Westwood winning the fifth, the Europeans had their noses in front early on but, as Patrick Cantlay and Xander Schauffele starred knocking in putts, four out of five holes fell to the Americans around the turn.
The home duo went on to win that one 2&1, securing a point for the second morning running and Schauffle, like Johnson, taking his haul to three out of three.
In winning the third straight session 3-1, the Americans moved to within five-and-a-half points of securing victory and, with 16 points still up for grabs, it was looking ominous for the Europeans.
Brooks Koepka/Daniel Berger lost to Sergio Garcia/Jon Rahm 3&1
Dustin Johnson/Collin Morikawa bt Paul Casey/Tyrrell Hatton 2&1
Jordan Spieth/Justin Thomas bt Viktor Hovland/Bernd Wiesberger two holes
Patrick Cantlay/Xander Schauffele bt Lee Westwood/Matthew Fitzpatrick 2&1