Bradley, who this week made his first team event appearance in 10 years, missed putts to clinch the Presidents Cup over the closing holes but got the decisive point when Kim missed an eight-foot birdie putt at the par-four 18th.
"They made the captain's job really easy and these guys played their hearts out this week, and they really played well on the back nine," said US captain Jim Furyk.
The US needed 4-1/2 points from 12 singles matches and wins for Xander Schauffele, Russell Henley and Patrick Cantlay along with a half-point from Sam Burns set the stage for U.S. Ryder Cup captain Bradley, who beat Kim 1-up with five other matches on the course.
Bradley, who this week made his first team event appearance in 10 years, missed putts to clinch the Presidents Cup over the last two holes but got the decisive point when Kim missed an eight-foot birdie putt at the par-four 18th.
"It's a fairy tale; it's a movie almost," said Bradley. "I just can't believe it. You just have to work as hard as I can, and good things happen."
While the Internationals swept Friday's session to draw level at 5-5, the Americans built up an 11-7 lead on Saturday that left their opponents needing 8-1/2 of the remaining 12 points to win the cup, a feat neither team has achieved in the event's history.
The US, a dominant squad of golfers all in the top 25 of the world rankings, including five of the top 10, took control early and never wavered even as the Internationals made a late push in a number of matches.
Furyk sent Schauffele out in the opening match and the world number two carded five front-nine birdies in his 4&3 win over Australian Jason Day for the first U.S. point of the day.
"My goal was just to set the tone, get red up on that board as early as possible, and I was able to do that," said Schauffele.
Burns and South Korean Tom Kim followed with the first tie in any match all week before Henley secured a 3&2 win over Im Sung-Jae in a match the American never trailed.
Japan's Hideki Matsuyama delivered the first full International point of the session when he birdied three of his final five holes to secure a 1-up win over Scottie Scheffler.
While Canadian Corey Conners added another point with a 5&3 win over Tony Finau it was too little too late as Cantlay, a 3&1 winner over Taylor Pendrith, and Bradley already had the upper hand in matches they closed out.