The Japanese star, who wore white and blue golf clothing, said he was delighted to have won on the Jack Nicklaus-designed course.
While the other leading challengers struggled in the final stretch, Na was in early at 13 following an impressive eight-under-par 64. Bubba Watson was one of those who faded; the overnight leader dropped out of contention after shredding a trio of shots on the 14th and 15th holes.
Matsuyama struggled at times but birdied the last to force a play-off.
The extra hole caused problems for both though, with Matsuyama's tee-shot landing in a bunker and Na driving into the creek on the left side of the fairway.
Na then missed right while the 22-year-old Matsuyama hit a spectator on the other side of the fairway. However the Matsuyama followed with a superb flop on and holed out for par and victory.
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