Perry, who shared second place in 2002, completed 54 holes with a 12-under 201 total.
The three-time winner on the PGA Tour last season sank a 33-foot birdie putt at the 18th hole to grab his one-stroke lead over Scott Piercy (66), who wasted an early five-shot lead in the third round.
"I kept leaving all of my putts short until the last hole, what a good place to make one there on the last hole," Perry said.
Kevin Na (66), Brian Gay (67) and Charley Hoffman (69) all share third at 10-under 203.
Second-round leader Nick Watney (72) slipped into a tie for 13th at 8-under 205 with Rocco Mediate (67), Cliff Kresge (68), and former Masters winner Zach Johnson (68).
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