The pair started the day tied and both had 6-under 66s to finish at 24-under 264 before McDowell prevailed when Singh missed a birdie putt on the third playoff hole.
It was unbelievable, McDowell said. Its a major relief to get it over with. Jeevs a fantastic player, a great guy and Im just glad I was able to hit one close to the flag at the last there, that was sweet.
The win gave McDowell his first European Tour victory since 2004 and the third of his career. The $2.9 million tournament at the Pinx Golf Club was sanctioned by the European, Asian and Korean Tours.
Irishman Paul McGinley had an eagle and five birdies in a 3-under 69 final round to finish third, two shots ahead of Japans Shingo Katayama.
Denmarks Thomas Bjorn, Johan Edfors of Sweden and Korean-American Anthony Kim were next at 14 under.
British Open champion Padraig Harrington struggled to a 74 on the final day and finished 14 shots off the lead.
Local favorite and world No. 5 K.J. Choi ended a disappointing 24th, 17 strokes off the pace.
Singh started his final round with birdies on three of the first four holes to quickly take a three-stroke lead. McDowell got back into it with an eagle at the 10th, but saw Singh take a one-shot lead with a birdie at 16.
However, the Indian bogeyed the par-3 17th, and both got par on the last to take the tournament into a playoff.
McDowell set up his birdie on the final playoff hole with a precise 7 iron to the green.
Ive worked unbelievably hard for this, he said. Ive been really patient, Ive tried to keep disappointment and frustration out of play, so its a really special feeling right now.