The 33-year-old Englishman, who led from the opening round, finished at 10-under 274
"I made some mistakes today, making it a little too close for comfort," Poulter said. "But it turned out well in the end."
The victory earned Poulter $833,330 and moved him up 19 places to 10th in the rankings of the European Tour's Race to Dubai.
Poulter sputtered midway through his final round with four bogeys, but a birdie on the 13th, capped by a 30-foot putt, put him back on track.
"I was getting angry," said Poulter, who won his first European Tour event since 2006 and 10th overall. "I felt I had to do something and I did, and it gave me a nice boost."
Players finished the third round and completed the fourth Sunday as the skies cleared and allowed the first full day of golf after three days of rain delays.
Australian players Scott Hend (69) and Adam Scott (68) finished two shots back in a tie for third. Phil Mickelson (71) and Ernie Els (72) finished six shots back at 4-under.
The Singapore Open is co-sanctioned by the European and Asian tours.