Stenson carded a final round of 68 at East Lake to win by three shots from Jordan Spieth and Steve Stricker and claim the first prize of US$1.4m (£875,000) and US$10m (£6.25m) FedEx Cup bonus.
The 37-year-old Swede, who had won just over US$13m (£8.1m) before arriving in Atlanta, had led by nine shots midway through the third round but bogeyed three of his last five holes to take a four-shot lead over Dustin Johnson into the final round.
That lead was down to one when Spieth birdied four holes in a row from the 13th to go with the hat-trick of birdies he had carded from the seventh, with Stenson dropping his first shot of the day on the 14th.
However, Spieth then bogeyed the 17th when his approach plugged in a greenside bunker, and Stenson crucially holed from seven feet for what proved a decisive birdie on the 15th.
World No.1 Tiger Woods carded a closing 67 to finish level par for the tournament and in a tie for 22nd place in the 30-man field.