Stenson, who started the day five strokes behind, parred the first six holes before storming home with six birdies to card a bogey-free six-under-par 66 at the punishing Sawgrass TPC.
He finished at 12-under 276, collecting $1.71 million for his seventh professional victory, his second in the United States.
Englishman Ian Poulter (70) claimed second place on eight-under, with Americans John Mallinger and Kevin Na another shot behind in a tie for third.
German Alex Cejka, who started the day with a record five-stroke lead, crumbled with a 79 to tie for ninth, a distant eight strokes back.
Accurate driving was the key to Stenson’s victory. He left his driver in the bag on all except one occasion, using his trusty three-wood to hit 13 of 14 fairways.
“It’s a course I really enjoy playing,” Stenson said. “It suits my game. I like to hit my three-wood a lot and I had my ball in great position today and it’s easy to play from there.
“I haven’t analyzed it yet, but it’s definitely one of the best final rounds I’ve done.
“I handled myself well these four days, putted well and stayed level-headed. Obviously it’s a great feeling to have won this championship.
“To hold off such a strong field is going to give me a lot of confidence going into the majors.”
He is the third European to win the flagship event on the United States PGA Tour, joining Spaniard Sergio Garcia (last year) and Scot Sandy Lyle (1987).
And Poulter made it a 1-2 European finish by winning the race for second place.
“I was pleased with how I finished the tournament off and my hat’s off to Henrik for putting his foot down and disappearing,” said Poulter, who was also runner-up at last year’s British Open, where Stenson tied for third with Greg Norman.
Stenson opened a three-shot lead when he birdied the par-three 13th and was four clear by time he got to the 17th tee.
However, no player can plan a victory speech until he finds dry land at the famous island green par-three, and Stenson spent considerable time on the tee before safely finding the putting surface.
Only then could he relax, and enjoy his victory march.
The 33-year-old Dubai-based Stenson came into the event ranked ninth in the world, so he was hardly a dark horse, but nor was he a name on everyone’s lips.
But he is now, after walking away with the richest tournament in golf.