Rose, the 54-hole leader, shot 3-under 67 and had a 15-footer for par on 18 that would have given him the win.
Bradley won his fourth career title, his third in a playoff, to deny Rose his third triumph of the season even though the runner-up effort was enough to see the Englishman atop the rankings for the first time in his career.
NEWTOWN SQUARE, Pa. - It was pointed out to Tiger Woods on Monday after he shot 65 at the BMW Championship that he had qualified for the 2019 U.S. Open at Pebble Beach, eliciting a smile and a quip: "Yep, I won't have to ask for one, " he said.
The event is the third of four tournaments in the PGA Tour's end-of-year FedEx Cup Playoffs and featured a field of 69 players from the top of the playoff standings. "A really solid round today is the difference of potential outcomes where I could do better".
On the first play-off hole, Rose's inexplicable par miss from all of four feet handed Bradley his first PGA Tour victory since August 2012.
Bryson DeChambeau, who had won the first two legs of the FedEx Cup playoffs, finished tied for 19th at Aronimink and enters the Tour Championship with the overall FedExCup points lead. "I don't know if that counts".
Bradley trailed by three shots going into the final round and atoned for a disappointing Sunday in New Jersey, where he had a chance to win the Northern Trust two weeks ago before shooting 78 in Round 4. "Was riding some momentum (after the Dell Technologies Championship) but all in all, just game kind of got a little off".
Bradley was a former user of the long, anchored putter and used it to win the 2011 PGA Championship - before anchoring the club to the body was outlawed by rulemakers in 2016. Delighted to be world number one. He is more likely to win the event and get his first victory of the season because he is only a couple shots off the lead.
For the sixth time in his career, Woods shot 263 or better. "But that second round. you can't shoot over par here and that threw me so much (further back)". That projects him to move up 22 spots into the 30th position in the FedEx Cup, which would bump out Jordan Spieth.
"It's scary when I look back, because I didn't know I needed this much improvement", Bradley said.
Five-time BMW championship victor Tiger Woods mounted another vintage charge, but a late back-nine stumble has been the story of his comeback season from spinal fusion surgery. A couple of holes into the final round, Woods is now just two strokes back. Spieth is the first player to violate the policy, which began a year ago.
That means he will have played only 24 tournaments this season.
Bradley and Rose finished a shot ahead of Schauffele, who shot 67, and former FedEx Cup victor Billy Horschel, who signed for a 64.