English stars Hull and Woad had been paired in each of the first four sessions of the three-day event — a first for a Solheim Cup — and only contributed a half-point between them.
But redemption came Sunday, with Hull leading from the front to beat Megan Khan, previously undefeated in singles, 3 and 2 in the first match.
Woad then went four up after nine holes against Auston Kim before going on to earn a more hard fought win 2&1, which prompted huge celebrations as it effectively sealed the return of the Cup to Europe.
Woad's two-foot putt on 17 to win her match saw her punch the air and jump into the arms of her teammates, who were flooding onto the green in celebration.
Within 10 minutes, Carlota Ciganda, who also grabbed the decisive point when Europe retained the Solheim Cup in 2023, officially got them to the victory target, completing a 4-and-2 victory over Jennifer Kupcho.
It was a sweet win as it had been her feisty American opponent who, on Saturday, had roared "Vamos!", somewhat provocatively after holing an outrageous 93-foot putt on the way to beating Ciganda in a spiky fourballs.
"Today I was really motivated to beat her," Ciganda said, "because I knew it was going to be important."
Strains of "Olé, Olé, Olé, Olé" drifted across the course as the last matches finished and the European team and staff celebrated with champagne.
"This feels so good," Europe captain Anna Nordqvist beamed.
"We just had a really good vibe all week. Everyone has been really good team-mates."
"She's been playing so good this week and not really getting anything off of it," Nordqvist said of Woad.
"But holing the winning putt, I don't think that's ever going to be hard to forget for her."
