Annika Sorenstam, the local favorite at Barsebck Golf & Country Club and World No. 1, set the table for Matthew's clinching point. A few minutes earlier, Sorenstam downed Solheim Cup rookie Angela Stanford, 3 and 2, to get the Europeans to 13 1/2 points.
Then it was up to Matthew, who had been controversially left off the last two European teams. Matthew knocked her approach to seven feet at 17 and when Jones missed a long birdie try, she walked over and conceded the point and the Cup to Europe.
'This is absolutely fantastic,' said European captain Catrin Nilsmark, who limped around on crutches all week thanks to a severe back injury. 'It has been a wonderful day and a wonderful week and I am so proud of my players and the way Sweden has hosted the event.'
'It rates up there for sure,' said Sorenstam. 'This crowd, I want to thank them all for coming, obviously for supporting us. It's been so great this week. It's a first-class tournament, first-class venue.'
Sorenstam has enjoyed an amazing 2003 campaign. She became the first women to compete on the PGA Tour in 58 years at the Colonial, completed the career Grand Slam with wins at the LPGA Championship and Women's British Open and now a spectacular Solheim Cup.
This was the third Solheim Cup victory for the European squad and its first since the 2000 staging at Loch Lomond.
The final score ended up with Europe claiming a 17 1/2 - 10 1/2 win, but not after some strange occurrences at the end of the event.
Once Matthew clinched the Cup for Europe, all other matches still on the course were conceded and the player ahead at the time of the concession received the full point. Some players weren't sure who conceded the match to whom or whether or not the matches were halved.
What it meant was that Cristie Kerr, who was 1-up through 15 holes against Suzann Pettersen, earned the full point for the U.S.
Laura Davies was ahead of Meg Mallon, Mhairi McKay was up on Beth Daniel and Patricia Meunier-Lebouc had the lead over Kelly Robbins in the anchor match so the Europeans took full points in those matches, which led to the lopsided score.
Laura Diaz, who missed a critical three-footer at 18 in Saturday's final fourball that would have earned a halve, atoned for the loss with a 5-and-4 drubbing of Germany's Elisabeth Esterl.
Sunday's single action came down to differing strategies by Nilsmark and American captain Patty Sheehan. Nilsmark owned a three-point lead heading into Sunday and stacked her lineup early. Sheehan went in a different direction as evidenced by the talented players who did not even get to complete their matches.
Advantage Nilsmark and Europe.
Janice Moodie seemingly made every putt all week and carried it over to Sunday when she dispatched American captain's pick Kelli Kuehne, 3 and 2, in the opening match.
Sophie Gustafson slaughtered Solheim Cup rookie and Sheehan's other pick Heather Bowie, 5 and 4. Iben Tinning of Denmark held on to beat Wendy Ward, 2 and 1, in a crucial match that ended on 17.
Then it was Sorenstam and Matthew, who shut the door on the Americans' chances at a historic comeback. No Solheim Cup team had ever overcome a two-point deficit with the singles to play and that record stayed intact.
Juli Inkster earned a convincing 5-and-4 win over Carin Koch in the second match and Michele Redman rallied to beat Spain's Ana Belen Sanchez, 2 and 1, for the Americans' only wins in the first seven matches.
'I take all the credit for losing today,' admitted Sheehan, who led the team to victory last year at Interlachen in Minnesota. 'I don't think I did such a good job on my lineup today. I probably should have put all the heavy hitters in the first seven or eight.'
After the Moodie, Gustafson and Inkster victories, things got tight for the Americans and it started with Ward. She had not played well all week and trailed 3-down around the turn.
Ward won the 11th with par and had a great chance to get 1-down at the 12th, but missed a five-footer for birdie. She eventually cut the margin to 1-down with a three-footer to win the 13th, but Tinning took over at No. 17.
Tinning drove into the right rough at 17 but fashioned a spectacular approach to two feet. Ward drove farther right at the hole and played her second into a greenside bunker. She blasted out to three feet, then missed the par save and conceded the match to Tinning.
'Iben played a pretty solid round of golf,' said Ward, who went 0-4 this year. 'She hit a heck of a shot in here on 17. I really wanted to make her have to make that putt.'
Redman came back to beat Sanchez, giving the U.S. a full point, but the writing was on the wall as Europe needed two points and both Sorenstam and Matthew were dormie.
Sorenstam flew out of the gate on Sunday with a 4-up lead through seven holes but Stanford hung tough. Stanford, who lost in a playoff for the U.S. Women's Open, won eight and nine with a birdie and par but Sorenstam won 10 when Stanford made a double-bogey.
Stanford won the 13th but Sorenstam holed an 18-footer for birdie and a win at 15. Sorenstam closed out the match one hole later and left Sweden with a 4-1 record.
'It was important to get the momentum going early and we did that,' said Sorenstam. 'The matches I played were very, very close and anything could have happened.'
Matthew overcame a 2-down deficit after two by not losing a hole the rest of the way. She won the 12th and seemed to match Jones with par every time it was needed.
'I was just so nervous coming down that last hole,' said Matthew. 'I knew it was kind of down to my game and I was trying to hit the green.'
Then all of the matches stopped, an unprecedented move since traditionally players complete the matches for pride. At last year's Ryder Cup, Tiger Woods and Jesper Parnevik played until the 18th when Europe had already won the Cup three matches earlier.
The U.S. now owns a 5-3 record in eight Solheim Cups and will have the chance to reclaim the Cup in 2005 at Crooked Stick near Indianapolis, Ind.