The United States won 13-7 to improve to 28-7-3 in the biennial competition, rebounding from a 10 1/2-9 1/2 loss in 2012 at Nairn in Scotland the Americans' only loss since 1996.
"I'm just really proud of my girls," said U.S. captain Ellen Port, from St. Louis. "As a captain, my goal was to keep them fresh and set them up for success. Not wear them out, not let them get tired of playing the course, because they are here so early, and all the late nights."
After Stanford's Mariah Stackhouse and Mississippi State's Ally McDonald halved their rain-delayed foursomes match with Stephanie Meadow and Georgia Hall, the United States needed only one point in the eight singles matches to regain the cup.
Talley, the U.S. Women's Amateur champion from Princeton, Kentucky, was quick to provide it, finishing off Law with a two-putt par on No. 15.
"When Captain Port put me out first, I wanted to get it done for my team, so they could play their hearts out today," Talley said. "We all wanted to play for each other this week. It was a privilege that I got to go out first. I was very happy that I got that opportunity and secured the point. It was definitely an honor."
Talley was a team-best 3-0-1.
"Dreams do come true, that's for sure," Talley said. "This was the best week ever. I'm just happy to play with my friends and to do it for my country is even better."
The Americans' 9 1/2-2 1/2 lead following the first four sessions was the largest since the playing format was expanded to five sessions over three days in 2008, bettering the 2010 U.S. mark of 8 1/2-3 1/2.
McDonald and Southern California's Annie Park also won singles matches for the U.S. McDonald beat 17-year-old Annabel Dimmock 4 and 3, and Park topped Gabriella Cowley 5 and 4.
"It's been amazing," McDonald said. "It was a blessing to have been chosen, and I just wanted to take advantage of this opportunity and make memories and play the best golf that I could, and I think this weekend, I played pretty well."
Stackhouse, the first black player in U.S. Curtis Cup history, halved her match with Eilidh Briggs.
Hall, Meadow, Gemma Dryburgh and Charlotte Thomas won singles matches for Britain and Ireland. Hall beat Southern California's Kyung Kim 3 and 2; Meadow topped UCLA's Alison Lee 2 and 1; Dryburgh edged Clemson's Ashlan Ramsey 1 up; and Thomas beat Central Kitsap High School product Erynne Lee 2 up. Lee is heading into her senior season at UCLA.
"So proud of the girls for how they rallied all day today," captain Tegwen Matthews said. "Especially, more especially when they knew the match was gone, and yet they never gave up. That could have put the chins really even further down. But no, we won the afternoon singles session. So that's a great way to finish and gives everyone a bit of a boost to say the least from a pretty disastrous two days."
The 2016 matches will be played at Dun Laoghaire in Ireland.