Team USA won six of the eight singles matches at Conwy Golf Club in Wales en route to a 12.5-7.5 success.
Caley McGinty was the only player on the home side to register a singles win in a one-sided contest.
Darling was denied a win in the top match despite being three up on Jensen Castle with four to play, only for Darling to bogey the 15th and 16th before Castle birdied the last to snatch an unlikely half.
Duncan, the star of last week’s AIG Women’s Open, took her match against Rachel Kuehn to the final hole, where the Scot ran up a double-bogey seven, gifting the point to Kuehn which also confirmed Team USA as the overall winners.
Great Britain and Ireland led 4.5-1.5 after the opening day of the women's amateur matchplay event but the US fought back on Friday to level at 6-6 heading into Saturday's singles.
"It feels amazing to have come here and to come away winners," said US captain Sarah Ingram. "We've had a spectacular week, beautiful weather.
"The people are amazing here, so welcoming and helpful and cheering us on as well as their own players. We're thrilled to have come away the winners."
It means the US have won 30 of the 41 contests, and it is their first away win in the biennial contest since triumphing at St Andrews in 2008.