Europe, trailing by two points after sharing the morning foursomes 2-2, won the afternoon fourballs 3-1 to set up a gripping conclusion at Finca Cortesin in Spain.
As holders, Europe go into the 12 singles on Sunday needing 14 points to retain the Cup - the USA need 14 1/2 points to regain the trophy.
In the top fourball, Leona Maguire and Charley Hull, who had been struggling with neck and shoulder pain on Thursday, led from the front and obeyed their skipper Suzann Pettersen's orders.
They were four up at the turn and, with Maguire making seven birdies in the 15 holes, closed out a decisive 4 and 3 victory over Ally Ewing and the previously unbeaten world No.3, Nelly Korda.
"Nelly and Ally are great players so we knew we had to bring our A games," said Maguire.
"Suzann made it clear we had to go out first and get a point on the board and the crowd has just been fantastic."
The second and third matches also turned European blue.
Emily Pedersen and Madelene Sagstrom defeated Andrea Lee and Rose Zhang 2 and 1, while Carlota Ciganda and Linn Grant triumphed by the same margin in the bottom match against Danielle Kang and this season's double major winner, Lilia Vu.
Ciganda, playing in front of her own Spanish fans, has won all three of her matches and made an all-but-clinching 15-foot winning birdie at the 16th.
Grant provided her own brand of exhibition golf with a phenomenal seven birdies over the front nine.
"I've loved playing in front of friends and family and everyone is playing great," said Ciganda.
Blue on the board
"It's been a great week so far and I just want us to win the Cup tomorrow."
The only USA point came from Angel Yin and Cheyenne Knight against Anna Nordqvist and Caroline Hedwall, who was playing in her first match of the week.
Hedwall holed a string of putts early on and Europe were two up after ten. But the Americans won three holes in a row from the 11th and went on to win by two holes.
"There was a lot of blue on the board but to get one red point was huge," said Yin, who made huge putts at 11 and 13.
"Cheyenne is a rookie but she's won two out of two. Amazing. We'll all be ready tomorrow."
The morning foursomes were shared 2-2 and perhaps it was a great finale by rookies Grant and Maja Stark that helped ignite Europe's afternoon charge.
All square with two to play against Kang and Lee, Stark holed a massive birdie putt to win the short 17th and Grant holed another lengthy putt at the 18th to match the American birdie and secure a vital one hole win.
"I'm out of words and I'm so proud," said a delighted Pettersen.
"But we're not there yet and there are 12 points up for grabs tomorrow.
"But we've made quite a comeback and now we're tied. Tomorrow we'll be ready to go."