As well as a first win on foreign soil, it was the first time Europe have retained the trophy since the competition was first played in 1990.
Swede Hedwall, so impressive in the
2011 victory at Killeen Castle in Ireland,
became the first player in the history of the trophy to win all five of her matches when she beat Michelle Wie with a birdie on the 18th to give Europe an unassailable 14-7 lead.
Matthew secured a par on the 18th to tie her match with Gerina Piller to earn an outright win.
She told Sky Sports: "I was shaking. My knees were shaking. I knew if I got a half we would win it outright.
"It beats [winning the Open in 2009]. Any time you can celebrate with your 11 team-mates it makes it more exciting, more fun."
Europe's total dominance of the fourballs on Saturday left the United States looking to become the first team to come back from more than two points behind, and produce the kind of performance that
Europe's men achieved in last year's Ryder Cup
to win the trophy.
At times, Meg Mallon's United States team was up in as many as seven matches but they never looked like generating the momentum to pull off a shock and it took just five of the 12 singles matches for Europe to retain the title.
Hull set the tone for Liselotte Neumann's Europe, winning five out of seven holes around the turn to overcome Creamer in comprehensive style.
Playing with Anna Nordqvist, beat Stacy Lewis/Lizette Salas (US) 4&2 in the foursomes.
Playing with Caroline Masson beat Angela Stanford and Gerina Piller 2&1 in the fourballs.
Playing with Anna Nordqvist, beat Jessica Korda and Morgan Pressel 2&1 in the foursomes.
Playing with Caroline Masson beat Michelle Wie and Jessica Korda 2&1 in the fourballs.
Beat Michelle Wie, one up in the singles.
only turned professional this summer
and her youthfulness was summed up by her getting former US Open champion Creamer to sign her ball for a friend after the win.
Hull told BBC Sport: "I gave myself high hopes and I just wanted to prove people wrong. I'm 17 and people were wondering if I could perform under the pressure but I go out and enjoy it, which takes care of the pressure.
"Before the match I just thought 'bring it' because I beat her on Saturday and I'd try to do it again."
Spaniard Ciganda moved ahead on the ninth against Morgan Pressel and picked up a comfortable win to make it 13-6, only for Lang to beat Azahara Munoz moments later to close the gap once again before play was delayed for almost an hour by the threat of lightning.
But Europe wasted little time after the break in wrapping up the win.
Hedwall's approach to the 18th left her with less than five feet for a birdie and when Wie missed with her attempt, the Swede drained her effort to retain the title.
Charley Hull on 'wicked' Europe win
"This is definitely the biggest moment of my life golf-wise," Hedwall said. "It's awesome. I was part of it at Killeen too but this beats it by far."
Veteran Matthew, 43, never led against Piller but pulled level with a par on the 17th and then another par on the final hole won it for Europe.
With the title already won, American Lexi Thompson completed a 4&3 win over Caroline Masson and Norwegian Suzann Pettersen missed a par putt on the 18th and halved her match with Lizette Salas.
Jodie Ewart-Shadoff overcame Brittany Lincicome 3&2 and Italian Giulia Sergas tied with Jessica Korda.
Beatriz Recari beat Angela Stanford 2&1 and Cristie Kerr and Karine Icher halved their match on the 18th.
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