Matsuyama, 22, emerged victorious in a wild finish to become the youngest champion of the prestigious $6.2 million event at Muirfield Village.
He joined a short list of Japanese champions on tour, after Shigeki Maruyama (three wins), Isao Aoki and Ryuji Imada.
"This is a future megastar," six-times major champion Nick Faldo said on the CBS television broadcast. "This man is strong physically, mentally and technically."
Matsuyama made his share of mistakes down the stretch, but also hit a series of precise approach shots as major champions Bubba Watson and Adam Scott fell away.
The young Japanese won with a par at the first extra hole of the sudden-death playoff, sinking a 10-foot downhill putt in front of tournament host Jack Nicklaus.
"We have a great winner. This young man is going to win a lot of golf tournaments," Nicklaus, the most decorated player ever with 18 major titles to his credit, told reporters.
"His first win in the United States, you've got to start somewhere and we're proud he's our winner. Twenty-two years, that's how old I was when I won my first tournament (the 1962 U.S. Open)."
Matsuyama (69) and South Korean-born Na (64) finished at 13-under-par 275, one stroke ahead of overnight leader Bubba Watson.
Na looked likely to come up short of victory when he posted his final score just as Matsuyama, Watson and Scott made the turn.
However, the three leaders all played the back nine over par and when Matsuyama also made a mess of the 16th and 17th holes, it seemed likely Na would claim an anti-climactic victory without even a playoff.
But cometh the hour, cometh the man, and Matsuyama rifled his five-iron to five feet at the par-four 18th and sank the putt dead center to become the first player ever to birdie the hole all four days of the tournament.
"I knew I had to make birdie so I took dead aim to the pin," he said.
Matsuyama did not need another birdie in the playoff after Na hooked his drive into the creek and had to take a penalty stroke.
Nicklaus praised Matsuyama's timing and temperament.
"I love his tempo. He has the ability to be able to play golf courses well within himself and doesn't have to push for distance and strength. His composure is very calm.
"I think you've just seen the start of what is going to be one of the world's great players over the next 10 or 15 years."
Matsuyama is not too young to appreciate the significance of winning the Golden Bear's tournament.
"To win my first PGA Tour event is enough, but to win it here at Mr. Nicklaus's course really gives me a lot of confidence going on and hopefully I'll be able to use this week as a stepping-stone to further my career," he said.
Matsuyama, the 2010 Asian Amateur champion, turned professional in April of last year and quickly established himself as a world class player, contending for victory at the British Open and winning four times on the Japan Tour to top the money list.
He may lack the charisma of compatriot Ryo Ishikawa, who is five months older and also a member of the PGA Tour, but he more than makes up for it with a swing that, despite a discernible pause at the top of the backswing, generates enormous power.
"One of my goals as a young guy was to win on the U.S. PGA Tour and now that I've done that my next goal now is to win one of the four majors," Matsuyama said.
"I hope the momentum of winning here will carry over to the U.S. Open."
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