Song of Korea first parred a testy 10-footer for par and then parred the final two holes to keep his overnight one-shot lead intact and win the coveted title, which returned to the circuit after an absence of three years.
Song carded 70 to total 12-under 272 and Spieth despite his week's best of 66 ended one short at 11-under 273.
China's Liang Wen-Chong, who missed a three-footer on 18th on Sunday, was third at 10-under 274. Spieth, who delayed his Sunday night departure to Monday, made no mistake with his final putt and then waited for news from Song.
Inclement weather, threat of lightning caused multiple delays during the week, forcing the Singapore showpiece to a Monday finish for the third time in 10 years at the Sentosa Golf Club.
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Song, who has finished runner-up on Japan three times and another three times on Korean PGA Tour, won his first professional title and it came after a titanic tussle against the World No. 1, who stopped one short of winning his first title in Asia and only the second outside United States.
"That one night felt like a week! It was crazy. I couldn't sleep and I was constantly thinking about putting throughout the night," said Song, who when he came to Sentosa at 7.30 am this morning, bravely holed his putt.
He went on to hold his nerve on the 17th and 18th for a card of 70 and a 12-under 272 total that left Spieth stranded at 11-under 273.
Song said:"I read the line well on 16 and just maintained my composure on 17 and 18. I knew the title was for me to lose as long as I don't make any silly mistakes."
"I went to the putting green to practice early in the morning as I knew I had to get that birdie to force a play-off. It was nerve-racking and I was happy I managed to stroke the ball well and it went in. I made some poor decisions in the middle two rounds as I was trying to do a little too much. But overall, it has been a great experience and I had a really good time here," said Spieth.
Chawrasia, runner-up at 2015 Hero Indian Open, had six birdies, four of them in last seven holes. He was Tied-38th. Himmat (70-69-73-70) at two-under 282 finished Tied-23rd and Rahil Gangjee shot 68-72-75-69 to finish even par 284 and tied-34th. Shiv Kapur ended the week at even par 71 and was tied 64th at 291.