Leading by two points heading into the final-day singles at Inverness Club in Toledo, the Scot’s side were up in eight of the 12 matches at one point before holding off a late fightback to win 15-13 as they became just the second European team to triumph on US soil.
After victories for rookie sensation Leona Maguire, Madalene Sagstrom and Celine Boutier, coupled with half points from Anna Nordqvist and Nanna Koerstz Madsen, Matilda Castren, the first Finn to play in the match, delivered the point that retained the trophy.
The win was then clinched by Dane Emily Kristine Pedersen as she triumphed in the anchor match, with the Europeans showing what they thought of Matthew’s contribution by singing “we love you Beanie, we do” as they celebrated.
Matthew played on the first European win on US soil in Colorado in 2013 and her place in Solheim Cup folklore has now been well and truly cemented after joining US duo Judy Rankin (1996 and 1998) and Inkster (2015 and 2017) as the only two-time winning captains in the event.
“Just an amazing team actually,” said the North Berwick woman. “They came out here and performed. I'm kind of lost for words actually at the moment.”
On winning as a captain in the US, she added: “I think it's even sweeter. It's certainly more nerve-racking watching. It's all down to the team really, it's if they play well, so all hats off to them.”
Capping a phenomenal performance as a first-timer, Maguire led the way for Europe as she posted a 5&4 win before further points were quickly added by Swede Sagstrom and Frenchwoman Boutier as they triumphed by 3&2 and 5&4 respectively.
Needing 14 points to retain the trophy, Nordqvist then edged Europe closer to that tally as she halved the top match before the Americans hit back through wins from Nelly Korda and Megan Khang.
However, Danish rookie Madsen delivered another half point before fellow first-timer Castren, holed a 10-foot par putt to win her match on the last to retain the trophy.
“I think I'm still shaking,” said Castren. “I was looking at the board and I knew it was going to be an important putt, and I wanted to make it. Me and Mikey (her caddie) read it perfectly and it went in. I'm just so happy right now.”
The win was then secured when Pedersen was guaranteed a half point as she led by three holes with three to play before just hanging on for a one-hole win as she matched Danielle Kang’s birdie at the 18th.
“I knew we had won after the 15th hole and I just wanted to celebrate,” said the Dane. “It was a bit of a fight in the end and it felt really good to hole that putt.”
In a match between two unbeaten players in the event, Maguire wasted no time showing that she was just as comfortable on this stage on her own as she had been alongside Mel Reid, thrice, and Georgia Hall, once, earlier in the week.
She holed 15-footer for an eagle at the second, celebrating that with a big fist pump. It was a mark of just how good her putting had been that it was a surprise when another hole-winning chance went begging.
But Maguire soon made amends by rolling in an 18-footer to win fourth with a birdie, holed another one from 12 feet to go three up after six and then knocked in a 10-footer at seventh to leave Kupcho wondering what had hit her.
Maguire, the first Irish player to compete in the match, went on to win 5&4, putting the first point of the day on the board and taking her personal tally for the event to an impressive four-and-a-half points, which constituted the best-ever debut in the event.
“Jen is a world class player. We've done battle many times in college,” said Maguire of her effort on the last day. “I knew I was going to have to play some really good golf to beat her today.
“Got off to a great start; that eagle on two really sort of set me up and holed some really nice putts, and just really kept my foot down all day.”
On her overall performance, she added: “I've been having a great year since June. Dermot [Byrne, her caddie] has been a tremendous help to me.
“He was a huge part of this week, keeping me calm, keeping me focused, hitting the right shots at the right moments, and I had two phenomenal partners in Mel and Georgia, as well.”
Sagstrom, who had been left in tears after being at the centre of a rules controversy in the second session on Saturday, ended the event feeling much better.
The Swede lost the opening hole to Ally Ewing, but, helped by a run of three out of five holes going Sagstrom’s way, she delivered another point with a 3&2 win.
I'm very happy right now. I didn't have the best start to the week,” said Sagstrom. “I was really happy Catriona decided to put me out first thing Sunday morning, just showing that she believes in me, showing that the team has got my back, so that was really nice.”
Boutier, who had shone on her debut on Scottish soil, delivered the goods again for her captain, winning five out of nine holes from the fifth as she crushed rookie Mina Harigae.
“I think I just didn't make a mistake today,” said Boutier. “I played really solid from the start.”
As had been the case four years earlier in Des Moines, Anna Nordqvist and Lexi Thompson found themselves leading the way for their respective teams in the concluding session.
In what is regarded as one of the best contests in this event, Nordqvist won the first four holes in 2017 only for Thompson to come storming back before Nordqvist stiffed her approach at the last as they eventually finished all square.
The opening hole was halved in bogeys on this occasion before a shank from Thompson helped Nordqvist, the AIG Women’s Open champion, edge ahead at the second.
The Swede still had her nose in front until Thompson won the eighth and ninth with back-to-back birdies, the latter raising a huge roar that echoed around the course.
It was advantage Nordqvist again with three holes to play but, after Thompson won the 16th with a birdie, it was a case of deja vu as the spoils were shared once again.
“We both played so good today,” said Nordqvist. “I wish I could have made a few more putts. I felt like I rolled the putter good.
“It's a huge honor to know that Beanie (Matthew) believes in me. She asked me last night if I wanted to go early or late, but I said, ‘I don't mind going early’. I enjoyed it.”
It then got a bit edgy for a spell, but the Europeans weren’t to be denied, with Matthew being hoisted into the air as the celebrations started on the 18th green.
"It feels unbelievable, I can’t believe it,” said the captain. “We knew it was going to be tough with only a handful of European fans here this week, but the players dug deep and I am so proud of them.”
Singles (European names first)
Anna Nordqvist halved with Lexi Thompson
Madelene Sagstrom bt Ally Ewing 3&2
Leona Maguire bt Jennifer Kupcho 5&4
Georgia Hall lost to Nelly Korda 1 hole
Celine Boutier bt Mina Harigae 5&4
Nanna Koerstz Madsen halved with Austin Ernst
Matilda Castren bt Lizette Salas 1 hole
Carlota Ciganda lost to Brittany Altomare 2&1
Sophia Popov lost to Megan Khang 3&2
Mel Reid lost to Yealimi Noh 1 hole
Charley Hull lost to Jessica Korda 3&1
Emily Kristine Pedersen bt Danielle Kang 1 hole