"I knew that Vijay was putting together a good round and playing well," the Argentinian said. "It was up to me to play well on the last two holes and I did that."
Cabrera started the day with a four-stroke lead, but shot a one-over 72 in the final round at Sentosa Golf Club.
Singh started six strokes behind Cabrera, but trailed by two shots after only seven holes on the 6,710-yard Serapong Course. The Fijian's advance began with an eagle on the fourth hole, a par-5 dogleg-left that sweeps around a lake. He also had four birdies and two bogeys.
Singh missed an eagle from about 20 feet on the final hole, but birdied to finish at 7-under 277. Cabrera sealed his win with a birdie on the same hole. He earned $634,000 for the victory at the $4million tournament.
"It was really a very, very tough day, very windy," Cabrera said. "I didn't strike the ball my best in the beginning of the round.
"But I worked very hard during the round and I got it together in the end and started hitting the ball very well in the last holes and I made it up."
Singh knew it would be difficult to catch Cabrera.
"I'm playing against a guy who is the U.S. Open champion and you can't expect him to make too many mistakes," he said. "I played well, made some good putts on the front nine and putted well all day. Just came one short."
Two-time defending champion Adam Scott had four birdies and as many bogeys to shoot a 71 and finish third, four strokes behind Singh.
"I missed a couple of greens and made bogeys and that seems to be how my year has gone," said the Australian, whose only victory this year came at the Houston Open. "I've not scrambled well enough to keep myself going in tournaments which was a case of that today."
World No. 2 Phil Mickelson, who had struggled in the previous round because of the heat, slid even further with a triple-bogey on the troublesome No. 3, and double-bogeys on the seventh, 13th and 16th to finish with a 79.
"It's tough to get the balls close to the hole because they are not stopping on the greens too well," he said. "The fairways are very tight and the rough is up and so it's a very good test because it tests every element of your game."
American rookie Jin Park, who came into the round four strokes off the lead in second place, dropped a few notches when he had four bogeys against just one birdie and finished fourth. Lee Westwood was fifth at 1-under after a 74.
K.J. Choi of South Korea had two birdies in the front nine, but fell behind with three bogeys and a double-bogey to finish in a tie for 14th at 5 over.