He had a four-shot lead when the final round began, but managed just 1-over-par 72 Sunday to avert a potential playoff.
"I am very, very happy to win the Barclay's Singapore Open," Cabrera said through an interpreter. "It is a world-class event with some of the best players in the world like Vijay, Ernie (Els), Adam (Scott) and Phil (Mickelson), so I'm very happy to have outplayed them to win the tournament."
Cabrera's winning total was 8-under 276.
Singh (67), a native of Fiji, needed to make an eagle to force a playoff, but could not convert, and was 7-under 277.
Scott (71), a two-time defending champion, finished third at 3-under 281.
Els missed the cut Friday, and Mickelson (79), who struggled with headaches and stomach cramps, was 23rd at 8-over 292.