After the teams finished singles play tied at 8, Kim and countryman Y.E. Yang edged Belgium's Nicolas Colsaerts and Italy's Francesco Molinari in the fourball playoff at The Empire Hotel and Country Club.
Colsaerts had a chance to match Kim's birdie, but missed a 5-footer.
Yang forced the playoff, beating Molinari 2 and 1 in the final singles match.
After falling behind 3 1/2-1/2 on Friday in the opening foursomes, Asia cut it to 4 1/2-3 1/2 in fourball play Saturday, and tied it with 4 1/2 points in the closing singles. Europe leads the series 4-2.
India's Jeev Milkha Singh pulled Asia even at 7 with a 1-up victory over Spain's Miguel Angel Jimenez, and Sweden's Henrik Stenson restored Europe with 1-up decision over Japan's Ryo Ishikawa. Yang then finished off Molinari with a halve on the 17th to send the competition to the playoff.
European playing captain Jose Maria Olazabal withdrew from his scheduled match against South Korea's Bae Sang-moon because of a neck injury, with each team receiving a half-point.
Because Asian captain Naomichi "Joe" Ozaki selected Thailand's Kiradech Aphibarnrat to sit if a European player withdrew, Bae ended up taking Kiradech's spot against Colsaerts, a match Colsaerts won 1 up when he took the par-5 15th with an eagle and halved the final three holes with pars.
In the other matches, Kim and Spain's Gonzalo Fernandez-Castano halved, Japan's Yoshinori Fujimoto beat Germany's Marcel Siem 1 up, and China's Wu Ashun halved with Italy's Edoardo Molinari.