The putt gave the Koreans a one-up victory over Americans Tiger Woods and Dustin Johnson.
The match-winner came after Kim holed a desperate nine-metre putt at he 15th to steal the advantage over Woods and Johnson who appeared to have the hole tightly in their grasp.
Kim and Yang, who had the look of a sacrificial partnership when the pairings were announced, then fended off the best Woods and Johnson could throw at them in the push to the finish to win a match that depended as much on nerve as skill.
The Korean victory came on a day of total contrast to the crushing heat and super-fast greens on which Kim and Yang had floundered.
In the opening foursomes match on Thursday, they went down 6 and 5 to Hunter Mahan and David Toms.
Kim then partnered Adam Scott to a defeat in Friday's four-ball while Yang suffered another stinging defeat in partnership with Robert Allenby.
International captain Greg Norman rested the pair for Saturday's morning foursomes and the move proved a master stroke.
Kim and Yang came out primed for an afternoon round played in almost constant rain, but the young Korean said he hadn't noticed.
"For me, the weather is no problem. I don't know if it is rain or sun," Kim said.
He also put the victory down to his faith in his partner.
"I think we trusted each other. That's the main reason why we won," he said through an interpreter.
The best overall round of the competition for the Internationals was set up by the South African pair Retief Goosen and Charl Schwartzel who took out the previously-unbeaten Bubba Watson and Webb Simpson 2 and 1.
Goosen and Schwartzel led from the opening hole, but went through a shaky stretch after being four up with five to play only to survive thanks to a par at the 17th which halved the hole and won the match.
The third International four-ball win came thanks to the veteran Korean KJ Choi and Australia's Geoff Ogilvy.
Ogilvy and Choi dragged themselves to the front at the 11th and then halved the final seven holes to cling to their one-hole victory.
Both Ogilvy and Choi lost their respective morning foursomes matches after which the United States led 11-6, the desperate situation steeling them for the afternoon.
"We had to bounce back this afternoon and we've done that," Ogilvy said.
"We are going to need a really big day tomorrow, but we are still in with a chance."
In the other afternoon matches, Aaron Baddeley and Jason Day continued their hapless Presidents Cup going down 2 and 1 to Hunter Mahan and Bill Haas and Adam Scott and Ernie Els lost to Jim Furyk and Nick Watney at the 18th.
- AAP
