Stenson, who held a nine-stroke lead early in the third round, saw his advantage dwindle to one shot Sunday before coming through with a birdie on the 15th.
The Swede then closed out with three straight pars to finish at 13-under-par 267, three strokes ahead of Jordan Spieth and Steve Stricker.
Stenson bested FedExCup runner-up Tiger Woods to become the first European to ever to win both the Cup and The Tour Championship.
Spieth's 6-under 64 was the second-best score of the day and earned him a share of second place along with Stricker (65) at minus-10.
Sole possession of fourth place at 9-under 271 went to Webb Simpson, who logged Sunday's best round of 7-under 63.