Singh completed the tournament at 7-under-par 277, one stroke clear of a pair of major champions.
'I could not have asked for more honestly,' Singh stated. 'I think I am a very fortunate man to win, those boys put a good effort out there. The golfing gods are on my side so I am breathing much better now.'
Padraig Harrington managed a 1-under 70 on Sunday, while Ernie Els closed with an even-par 71 to share second place at minus-6.
Rory McIlroy and David Gleeson both closed with 69s to share fourth place at 5-under-par 279. Charlie Wi took sixth at minus-4 after a final-round, 1-over 72.
Third-round leader Chapchai Nirat stumbled to a 7-over 78 in the final round to share seventh with Thomas Bjorn (74) at 3-under-par 281.
World No. 3 Phil Mickelson took ninth at minus-2 after shooting 75 on Sunday.
Singh, who trailed by five shots starting the final round, got off to a flying starting with birdies on one and two at Sentosa Golf Club. After four straight pars, he converted his third birdie on the par-5 seventh.
The 60th-ranked player in the world moved to minus-9 with a birdie on the par-4 11th. Singh held on for the win despite bogeys on 13 and 16. He parred the final two to hold off Harrington and Els.
Harrington birdied three of the first four holes, but was done in by a double-bogey on the par-4 16th.
Els parred the first 11 holes before tripping to a bogey at the 12th. He atoned for that mistake with a birdie on 16, but closed with a pair of pars.