The American started the final round three shots behind Fleetwood and come the 15th hole, that buffer remained. But Bradley rolled in two birdies over the last four holes, including a 35-foot putt on the 15th, while Fleetwood bogeyed the 15th and 18th.
Bradley hit his 9-iron to six feet on the last and nailed the putt for the victory. Not once had he led the tournament until it counted.
"Of all the shots and all the putts I hit, I think I'm going to remember that one the most," the 39-year-old told the press after.
Meanwhile, Fleetwood - a seven-time winner on the DP World Tour - let his best chance at a PGA Tour win slip.
"I'm upset now, I'm angry," said the Englishman.
"When it calms down, look at the things that I did well, look at the things that I can learn from. The most stupid thing to do and the worse thing to do would be make a week like this a hindrance to what you do going forward. Right now I would love to just go and sulk somewhere and maybe I will. But there's just no point making it a negative for the future."
Bradley was named US Ryder Cup captain for the September team competition. Now with two wins since last August, he may very well be playing.
"This changes the story a little bit," Bradley said about his Ryder Cup role.
"I never would have thought about playing if I hadn't won. This definitely opens the door to play. I don't know if I'm going to do it or not, but I certainly have to take a pretty hard look at what's best for the team."
Meanwhile, Scottie Scheffler - who had a share of the 36-hole lead until a 72 in the third round - closed with a 65 and tied for sixth with Rory McIlroy, who also shot 65. They were three shots behind Bradley.