With the light fading on the Bernardus course in the Netherlands, Jennifer Kupcho holed a nerve-shredding putt from the edge of the 18th green to snatch a point and leave the teams tied at 8-8.
Europe had come into the afternoon session with all the momentum, looking to extend an advantage of 7-5 after a tense morning of foursomes.
Fresh from taking down world number one Nelly Korda in the early session, Europe sent out Swedish pair Maja Stark and Linn Grant against in-form Americans Megan Khang and Lauren Coughlin.
And on the very first hole, Stark conjured the shot of the competition so far, her approach to the green on the par four dropping straight into the cup for an eagle.
The match swung back and forth, with neither pair able to sustain a telling lead, but three birdies in a row from the 11th gave the Swedes a two-hole lead.
Fittingly, it was the red-hot Stark who drained her putt on the 17th for a 2&1 win that meant Europe would at worst be level heading into the singles.
"It's so nice when you stand over a putt, and you know that... you have it to win the match and then you actually do it. That's the best feeling," said Stark.
Europe captain Anna Nordqvist made the bold move of sending out Charley Hull and Lottie Woad second after they had suffered a 6&5 drubbing in the morning foursomes - one of the heaviest defeats in Solheim history.
The top-ranked pairing continued to labour, however, with a frustrated England star Hull struggling with her putter, as the US pair of Yealimi Noh and Andrea Lee secured a 1-up victory.
The third match saw Auston Kim and Rose Zhang from the US dominating Nastasia Nadaud and Leona Maguire, never slipping behind and cruising to a 3&2 win.
'Great finish'
As on Friday evening, the last pairing proved critical, with Carlota Ciganda and Celine Boutier taking on Kupcho and Lindy Duncan.
Ciganda continued her fine form from Friday, holing two long-range putts on the front nine to put the European pairing in the box seat.
Another pressure putt from the pumped-up Ciganda on the 14th gave them a two-hole lead, the Spaniard slapping her chest to whip up the boisterous Dutch crowd.
But an extraordinary 90-foot putt from Kupcho on the 17th clawed the Americans back into contention, and they headed up the last hole all square.
Kupcho repeated her heroics with another monster, winning the match and sending the whole US team into raptures around the green.
"That was amazing. Great finish to the match," said Kupcho as the crowd chanted her name.
The US are hoping to win the trophy on European soil for the first time since 2015. They lead the overall series 11-7.
It will boil down to Sunday's singles, where all 12 players face off for the crucial points that will decide the winner.
The US are the current holders, meaning they need 14 points to retain the cup. Europe need a minimum of 14.5 points to regain the trophy.
