The defending champions won six of the eight points available on Saturday to open up a commanding 11.5-4.5 lead over the United States and move within three points of outright victory.
It was a day of high drama and tension, with players arguing and the action being paused at times due to the boorish behaviour of a raucous New York home crowd.
Yet Luke Donald's side rose above the distractions to deliver a near knockout blow to the shellshocked hosts.
Europe tightened their grip with a 3-1 victory in the morning foursomes and for some time a fourball clean sweep looked possible until the hosts clawed the second session back to 3-1.
Emotions boiled over as Tommy Fleetwood and Justin Rose thrashed Bryson DeChambeau and Scottie Scheffler, while Rory McIlroy defied taunts to deliver another telling point.
World number two McIlroy was heckled throughout the day and shouted at one fan to "shut the f*** up" as he prepared to take a shot during his morning foursomes win.
He remained a target in the afternoon and both he and partner Shane Lowry needed to pause on numerous occasions as comments were aimed at them as they addressed the ball in their match against Justin Thomas and Cameron Young.
Thomas appealed for calm on their behalf at times and extra police were also needed to keep order.
Despite the frenzied atmosphere, the Irishmen pulled through to win a tense, tight encounter by two holes.
Ultimately a birdie two by McIlroy on the 14th proved crucial but it took some nerveless putting down the stretch to hang on to the lead before victory was secured on the last.
"Look, when you play an away Ryder Cup, it's really, really challenging," McIlroy said.
"It's not for me to say. You know, people can be their own judge of whether they took it too far or not. I'm just proud of us for being able to win today with what we had to go through."
Temperatures were also high as Rose and Fleetwood claimed a 3&2 win over world number one Scheffler - suffering a remarkable fourth defeat from four - and the fiery DeChambeau.
Rose was the key figure, winning four holes thanks to some clinical putting, but an argument broke out between Fleetwood and DeChambeau after the 15th was halved.
The incident was sparked by Rose asking DeChambeau's caddie to move out of his eyeline as he putted and the pair needed to be separated as they walked to the next tee.
Yet there was no way back for the American pair and the match ended - with handshakes all round - after halving the 16th.
It was Fleetwood's second win of the day, having successfully combined with McIlroy in the morning, and it looked like Jon Rahm could follow suit.
The Spaniard and Sepp Straka led by one after 16 against JJ Spaun and Xander Schauffele but late errors saw them surrender the last two holes to lose by one.
Yet while that took some gloss off the day for Europe, it was immediately countered by Tyrrell Hatton and Matt Fitzpatrick snatching victory on the 18th.
The final match of the day had been tame by comparison until exploding into life as Fitzpatrick played a brilliant bunker shot to within inches of final hole.
Hatton, summoned only at the last minute after Viktor Hovland pulled out with a neck injury, then pitched to a similar distance and the Europeans took a one-hole win.
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