Trailing 7-3 after Friday's foursomes, the Thongchai Jaidee-captained Asian team won six and halved two of the 10 singles matches to tie the scores at 10-10 for a share of the spoils.
Spain's Gonzalo Fernandez-Castano and Hideto Tanihara of Japan were the last men on the course and both had a chance to wrap up the tie on the final hole but after missing tricky birdie putts, their match and the teams finished all-square.
Thai duo Thongchai and Kiradech Aphibarnrat and Indians Anirban Lahiri and Gaganjeet Bhullar, South Korea's Kim Hyung-sung and Siddikur Rahman of Bangladesh all won their singles matches for Asia.
"Every part of my team was unbelievable to come back, fantastic," an elated Thongchai told reporters. "Everyone played really well. I think the match is unbelievable, it was a good finish.
"To end on the last, and on the 18th hole, it's fantastic. I have never seen a match like this. It's very close and amazing.
"We had a good draw and good pairings, I think that's the key point."
Europe's Spanish captain Miguel Angel Jimenez and Dutchman Joost Luiten were the only two winners for their team.
Jimenez needed to dig deep to beat local favourite 23-year-old Nicholas Fung with a birdie on the 18th hole.
"It's an amazing day of golf," the 50-year-old said. "It's been very tough. At the end of the week, the European team did not win the tournament but the Asian team, they played very well.
"As I said in the prize giving presentation, Asia, Europe, they both win, nobody loses."
Welshman Jamie Donaldson, who partnered Graeme McDowell to victory in the fourballs and foursomes, gave up a four-hole lead over Prayad Marksaeng and had to be satisfied with a half point.
"I played so well at the start," said the unbeaten Donaldson, whose tally of two-and-a-half points in the tournament was matched only by Jimenez.
"I flushed it for nine holes and then I don't know if the heat got to me a little bit, but I hit some shocking shots and gave him a few holes.
"It was good to get a half in the end. It was important to hole that putt for the team and for my match, but I made it very difficult."
The tournament will return to Malaysia in 2016 but the course for the second running of the event has yet to be finalised.
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