Despite opening with a bogey, Garcia bounced back with a birdie on the second hole and notched three in a row between holes four and six to jump out to 11 under par.
He remained there through nine holes, two clear of three Americans who were chasing hard.
Justin Thomas (nine holes), Chris Kirk (eight holes) and Kevin Kisner (eight holes) all were at nine under.
Seven players, including world number one Rory McIlroy (15 holes) were three off the pace at eight under.
Garcia had been battling a cold putter all tournament long but on Sunday he knocked in three birdie putts from six feet and another from 27 feet to take control.
He was vying to become just the seventh player to win the tournament multiple times, and the sixth to win twice at Sawgrass.
Former world number one Tiger Woods completed four rounds in back-to-back tournaments for the first time in 18 months but he will continue his drop in the rankings.
Woods, who had plummeted to 125th on the world list prior to the tournament, can at best hope to be 129th after his final round even-par 72 left him at three-over-par 291 on Sunday.
Currently tied for 69th, he is heading for his worst finish in the PGA Tour's flagship tournament, behind his tie for 39th in 2003.
(Editing by Gene Cherry)
