Stenson tapped in an eagle putt on the tournament's 72nd hole to finish off a bogey-free 8-under-par 64 in the final round. He was 25-under 263 for the tournament.
Ian Poulter shot 66 Sunday and ended up second at 19-under and Victor Dubuisson turned in a 71 and finished third another two strokes back.
Joost Luiten, firing a final-round 66, ended up fourth at 16-under while the high-profile trio of Rory McIlroy (67 Sunday), Luke Donald (67) and Lee Westwood (68) tied for fifth 10 strokes behind Stenson. McIlroy was the tournament's defending champion.
Stenson took a one-stroke lead into the final round and kept his advantage with four birdies in the first seven holes Sunday. He added two more at Nos. 12 and 14 and was well ahead before the eagle at 18.
Stenson had 25 birdies and the eagle against a pair of bogeys for the tournament.
"I played so well this week," Stenson said. "I knew the guys would try to catch me, especially Ian who never gives up. I wanted to stay ahead of him and I managed to do that."
Sunday marked the eighth European Tour win for Stenson, although it was the first on that tour in a year. He won the Deutsche Bank Championship and Tour Championship in September on the PGA Tour.
Stenson is the first golfer to the FedEx Cup and Race to Dubai in the same year.
The Race to Dubai title brings with it a $1 million bonus for Stenson, who also won more than $1.3 million with the tournament championship. He won $10 million for finishing first in the FedEx Cup standings.
Swim Week Miami Beach 2014 [PHOTOS]