The 48-year old Perry, who led after each of the first two rounds, trailed by a stroke to Paul Goydos heading into Sunday.
But he shot 32 on the front nine and was up by five strokes heading to the par-4 15th.
Goydos made a 20-foot eagle putt from the fringe on 15 and birdied 16. But he missed his birdie putt on 17 to the right.
Perry birdied 15, and put the tournament away by making birdie on 17 after hitting a 164 yard approach to within eight feet. His bogey-bogey finish at Augusta National kept him from winning the Masters Tournament in April.