Europe won the last three singles matches to seal a sensational 14½-13½ Solheim Cup victory over the United States at Gleneagles.
Bronte Law, who moments earlier won her match on the 17th, sprinted up the 18th fairway to join the celebrations after wildcard pick Suzann Pettersen holed an eight-foot putt on the last to win the trophy.
"She got a bit of stick for getting that pick, but it shows she was the right one," said Europe captain Catriona Matthew.
"For it to come down to the last game was amazing. I could barely watch, it's far worse watching.
"Everyone will remember that final putt but we had to get there. It's been a great week, with great performances throughout the team."
Pettersen later confirmed her retirement from the game, adding: "This is the perfect end to my career."
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Norwegian Pettersen was originally selected as a vice-captain after taking time out of the game in November 2017 to have a baby.
But after returning to play earlier this year, Matthew gave the 38-year-old world number 665 a surprise ninth Solheim Cup appearance.
And she repaid her captain's faith with a nerve-shredding victory on the final green.
American Marina Alex missed a 10-foot putt to halve her match with Pettersen to earn a 14th point that would have seen the US retain the trophy.
While Pettersen sized up what she thought would be a putt to win her match to put Europe on 13½ points, Law was sealing that point back on the 17th.
That suddenly meant a Pettersen birdie would seal the win, while a miss would have seen the US reach 14 points and retain the cup, but the Norwegian held her nerve to spark wild celebrations on the green.
Pettersen - at the centre of controversy over the concession of a putt in the 2015 match - later admitted she did not know her putt was to win the trophy.
"It really was a big blur," she said. "I didn't know. I was just trying to make a birdie."
Europe seal unlikely win
This is a third home victory from three matches played in Scotland and is Europe's sixth out of 16 editions of the Solheim Cup.
They led 4½-3½ after day one's alternate shot foursomes and fourballs but the US won Saturday's matches by the same margin to leave the Solheim Cup evenly poised at 8-8 going into Sunday's 12 singles matches.
And the trophy looked set to be heading back to the US after both Korda sisters won matches from behind.
Nelly Korda was three down after nine holes but four birdies on the back nine saw her beat Caroline Hedwall two up.
Jessica Korda also trailed early on but three birdies in five holes from the 12th saw her complete a 3&2 victory over Germany's Caroline Masson and put the US 12-11 ahead.
England's Charley Hull, who was one up playing the last, hit a poor chip that cost her the win over Megan Khang and when Dutchwoman Anne van Dam missed a putt on the last to hand Lizette Salas another point, the US were 13½-11½ ahead.
However, Sweden's Anna Nordqvist was four up against Morgan Pressel and she halved the 15th to draw Europe to within a point.
Law then won the par-five 16th with a birdie and when Ally McDonald, a late replacement for the injured Stacey Lewis, bogeyed the next, Europe had a levelling point.
Europe pegged back after strong start
Spain's Carlota Ciganda picked up the first European point when she birdied the last to beat Danielle Kang.
That point was quickly followed by two more. England's Georgia Hall and France's Celine Boutier, who combined to win three points on the opening two days, made it four wins from four this week with 2&1 victories.
Hall beat world number three Lexi Thompson and was immediately embraced by Matthew and Europe vice-captain Laura Davies.
They all then waited for Boutier, who was playing in the match behind, and there were more joyous hugs as thousands of fans celebrated round the green.
However, Angel Yin was never behind in her 2&1 victory over Azahara Munoz, while Brittany Altomare crushed Jodi Ewart Shadoff 5&4 to pick up another American point.
Jessica Korda, who was unbeaten in the competition, said: "Unfortunately we didn't get the win but what a day for women's golf."
US captain Juli Inkster said: "Europe played great and we tip our hat to them but now we move on to Toledo for the 2021 Solheim Cup."