The USA needed 4-1/2 points from the 12 singles matches and wins for Megan Khang, Rose Zhang, Allisen Corpuz and a half-point each from Andrea Lee and Lauren Coughlin set the stage for Vu, who sealed it with just two other matches on the course.
"I mean, this has been everything. I have a picture of the US team winning the Solheim Cup a while back, so it's on my wall in my room," said Vu.
"So this is a dream of mine, and so happy that I was able to do that for them."
Vu trailed Valenzuela with two holes to play as Europe mounted a fierce charge on the final day but the American capped her round with a pair of birdies, including at the last where she tapped in after a brilliant approach shot.
It marked the Americans' first win in the biennial match-play competition since 2017 and denied Europe from lifting the Solheim Cup trophy for an unprecedented fourth consecutive time.
The triumph did not come without some sweating as Europe, who trailed 10-6 to start the day and needed a record-equaling comeback to retain the Solheim Cup, struck first when England's Charley Hull beat world number one Nelly Korda 6&4.
While the USA won three of the next four matches, Europe refused to back down and eventually pulled to within 14-11 with three matches left on the course before Vu secured the win after Valenzuela was unable to sink her 30-foot birdie putt at 18.
"I mean, we gave them a run for their money. I don't think anyone expected us to be here at 2:30 and to still have a chance," said European captain Suzann Pettersen.
"It's kind of hard to believe that we actually had a chance with kind of that poor of a start, giving them such a head start."
Lexi Thompson, playing in her seventh and potentially last Solheim Cup, had a chance to secure the winning point but missed a 12-foot birdie at the 18th before Coughlin missed a 15-footer at the same hole and settled for a half point.
"It really could have gone either way," said US captain Stacy Lewis.
"It's crazy there at the end kind of how it all unfolded. I was just hoping and praying it went our way."
The USA lead the overall Solheim Cup series 11-7-1, with the one tie coming last year in Spain. The 2026 edition of the Solheim Cup will be at Bernardus Golf in Cromvoirt, Netherlands.