South Korean Kim Kyung-tae rolled in a 15ft birdie putt on the 18th, the first playoff hole, as he and compatriot Yang Yong-eun saw off Belgian Nicolas Colsaerts and Francesco Molinari of Italy in the fourball decider.
Asia's second win in the sixth edition of the annual contest loosely based on the Ryder Cup model then drew a 'Gangnam Style' celebratory dance from Japanese captain Joe Ozaki.
"I am so proud of all my players, but especially K.T. Kim. It was a great Royal Trophy and a great way to finish," Ozaki said during the presentation ceremony.
The narrow defeat capped a disappointing day for Ozaki's opposite number Jose Maria Olazabal, the Spaniard forced to pull out of his singles match before a ball was hit on Sunday because of a neck injury.
With Olazabal's withdrawal, each side added half a point to their overnight tally to leave the scores at 5-4 in Europe's favour with 8 1/2 needed from the remaining seven singles matches to claim the title.
Asia, who had trailed 3 1/2-1/2 after the opening day foursomes, began strongly on Sunday as they quickly raced into the lead in a majority of the matches before the European players found their form.
Colsaerts recorded the first playing point of the day when he edged Korean Bae Sang-moon on the 18th hole.
Spain's Gonzalo Fernandez-Castano then holed an eight-foot birdie putt on the last, one of three he made over the final four holes, to tie with Kim. Their half point making it 6 1/2-4 1/2 and leaving Europe within sight of victory.
But the Asians fought back and Japan's Yoshinori Fujimoto, who had been three down after 11 holes, rifled in a sharp approach to the last to overhaul German Marcel Siem and win 1-up to give the hosts their first victory of the day.
China's Wu Ashan should have added a second as he led Italian Edoardo Molinari by three after 13 holes but the Italian fought back to claim a precious half point and make it 7-6.
Europe were ahead in two matches and were still on course for victory but India's Jeev Milkha Singh, who celebrated his 41st birthday on Saturday, rolled in two long putts on 16 and 17 to head down the last 1-up on Miguel Angel Jimenez.
The Indian kept his nerve to get up and down for a par on the last after missing the green to record the narrow victory over the Spaniard and tie the scores at 7-7.
Asia then went ahead 8-7 as Yang beat Francesco Molinari in the final match 2&1, the only game not to go down the last, but Henrik Stenson ensured a playoff would be required as he survived a late wobble to edge Japan's Ryo Ishikawa 1-up on 18.
"You saw how close this match was by the fact six of the seven singles matches came down to the final hole," Olazabal said.
"The margins between victory and defeat are tiny and I have told my players I am very proud of them and they should leave with their heads held high." (Reporting by Patrick Johnston in Singapore; Editing by John O'Brien)