The 37-year-old Swede moved to the top of the FedEx Cup standings after two playoff events, assuring him his first trip to the Tour Championship and a clear shot at the $10 million prize.
"I'm just pleased I won here," said Stenson, who tied the tournament record at 22-under 262. "This was a big goal of mine to win a golf tournament after all those nice finishes. My family is here. I'm going to see my kids in a little bit. It's all good."
Stenson's win was only part of the high drama Monday, so much that Tiger Woods became an afterthought. He closed with a 73 and tied for 65th.
Stricker's third runner-up finish this year allowed him to move into the top 10 and qualify for the Presidents Cup team, despite playing a part-time schedule. That put the 10th spot up for grabs between Webb Simpson and Zach Johnson, who were playing together on the other side of the course.
They were tied at 8 under big advantage to Simpson until the former U.S. Open champion dropped two shots on the last four holes. Johnson faced a 25-foot birdie putt on his last hole that determined whether he made the team, and he poured it in the middle.
Last week Johnson gave up a chance to earn points by skipping The Barclays to be in his brother's wedding.
Lost in all this commotion was Jordan Spieth, the 20-year-old Texan dressed in a shirt with the Dallas Cowboys' silver-and-blue colors. He went birdie-birdie-birdie-eagle at the end of his round for a 62 right before the rain delay. With such soft conditions, his 17-under 267 was never going to hold up. Spieth wound up tied for fourth, and is No. 10 in the FedEx Cup standings.
Henrik Stenson -22
Steve Stricker -20
Graham DeLaet -18
Jordan Spieth -17
Matt Kuchar -17
Kevin Stadler -17
Sergio Garcia -17