The 37-year-old Swede also moved into first place in the FedEx Cup playoff standings with the victory, surpassing Tiger Woods for the overall lead.
Stenson, who won on the PGA Tour for the first time in over three years, finished at 22-under 262 in a Monday finish to tie the tournament scoring record at the TPC Boston.
“I’m just pleased I won here,” said Stenson. “This was a big goal of mine to win a golf tournament after all those nice finishes.”
American Steve Stricker, 46, finished two shots back in second place.
Stricker’s performance earned him a spot on Team USA after he improved to seventh from 11th in the President’s Cup standings.
Canada’s Graham DeLaet shot 69 to finish alone in third and 54-hole round leader Sergio Garcia, of Spain, shot a two-over 73 to tie for fourth with three Americans, Jordan Spieth (62), Matt Kuchar (66) and Kevin Stadler (68).
The Deutsche Bank event is the second leg of the four-tournament FeEx Cup playoffs which until Monday was led by Woods.
Woods stumbled to a two-over 73 Monday and finished in a tie for 65th.
“It wasn’t my week. I didn’t play well and didn’t make anything,” Woods said. “I didn’t have it today.”
The top 70 in the FedEx Cup standings advance to the third playoff event, the BMW Championship, which begins September 12.
Heavy rains all week led to low scores and plenty of delays, including two more on Monday.
The third round was completed in near darkness after a lengthy weather delay. Some players had started their third rounds, but the long stoppage forced organizers to erase that play and have players go out in threesomes of split tees.
Stenson, from Gothenburg, posted his first win on the PGA Tour since the 2009 Players Championship by rolling in six birdies in a Monday finish.
Stenson finished second at The Open Championship and the World Golf Championships-Bridgestone Invitational followed by a third at this year’s PGA Championship.
On Monday, Stenson made bogey on No. 2 but then birdied five straight holes beginning at No. 4. He compiled a three-shot lead through eight holes.
“It’s been long, hard work getting back to this place,” he said. “There’s no magic, no quick fix. It’s just hard work.”
Zach Johnson joins Stricker on the President’s Cup team. Johnson closed with a birdie on his final hole Sunday and a 66 which tied him for 27th.
He finished 10th and earned the final automatic qualifying spot for the American Presidents Cup team. US skipper Fred Couples will name his captain’s picks on Wednesday.
“I stayed in my process,” said Johnson. “I stayed just playing and hitting shots. I had a good day today. I missed some short putts, but I made some long putts. It was an odd day.”
Garcia has now won just three of the last 11 times in which he owned at least a share of the 54-hole lead.
He had both the 36-hole and 54-hole leads but stumbled to five bogeys on Monday.
“I just wasn’t comfortable,” Garcia said. “I wasn’t able to trust myself as I did the first few days.”