He is on the brink of becoming world No 1 for the first time in his 20-year career after play was washed out at the BMW Championship in Pennsylvania.
Monday's victory marks the end of a six-year slump for Bradley, the 2011 PGA champion, who dipped as low as 122nd in the world in 2016.
It will be his first appearance in the season-ending tournament in five years. "It was really kind of unusual because I don't normally look at leaderboards, but I looked all day and I felt so solid", Bradley said. "I'll represent the United States over there (in France for the Ryder Cup) and also compete with the top players on the tour".
Bradley, the 2011 PGA Championship victor, had not won since taking the WGC Bridgestone Invitational.
Englishman Justin Rose has become the World number one player in the latest Golf Rankings. Rose chose to putt his ball and left himself a knee-knocking five-footer, which he missed, allowing Bradley to tap in for the victory. Only two players bettered his 65 with 64s.
"It's so gratifying to get what comes with hard work", Bradley said. "You look at the scores, 20 under par".
He opened the round with a birdie on the first hole, and then added back-to-back birdies on No. 5 and 6, getting to within two of the lead early. But the 14-time major victor carded a 65 and ultimately settled for a share of sixth at 17-under.
By already sitting out of the first FedEx Cup event at the Northern Trust, and missing the Dell Technologies Championship, it unfortunately ruined his chances to be the overall FedEx Cup Champion.
Phil Mickelson would be 15th in the standings, and Woods would be 24th. But he was second in strokes gained, approach to the green, 13th in strokes gained, around the green, and 22nd in strokes gained off the tee.
His final round was steady in the extreme, nine greens in regulation on the front nine, nine pars.
"To have a chance to win again this year, it's a very positive feeling". To bogey the 72nd hole and to get into a play-off is obviously nothing to be happy about, but the putt I had to win was the best putt I've ever hit to try and win a tournament.
Spieth, who entered the BMW at 27th in FedEx Cup points, finished the event at minus-3 and slipped the 31st in the points standings. He made that for par to finish the third round in sixth place, three shots out of the lead. Spieth won the FedEx Cup in 2015.