Rose, like Bradley, failed to par the last in regulation as a 20-footer lipped out and he also bogeyed the hole in the play-off after a three-putt.
Rose missed the fairway again on the first playoff hole-18 again-and his approach bounded off the grandstand right of the green, finishing just off the putting surface.
Bradley, 32, burst onto the scene with a major victory at the 2011 PGA Championship, but until Monday had not won since 2012. His first putt bounced in the fringe and finished five feet short, then his par effort was left the whole way. To win and to put everything together when I didn't know if I was going to win again, to get to the Tour Championship, to have them here and have what's going on in my life is just so incredible. Bradley, who shot a final round 6-under 64 to finish at 20-under 260, thrust his arms toward the grey sky and drizzle in celebration and waved his family toward him.
Rose ascended to the No. 1 ranking in the Official World Golf Rankings and became just the 22nd golfer in history to do so. "It made me feel calm, which is rare".
"It's boyhood dreams", he told the Golf Channel of passing Dustin Johnson and Brooks Koepka for the No. 1 ranking.
After Sunday's wet weather postponed the final round, overnight leader Rose got off to a shaky start in defence of his one-shot advantage with a bogey on the first hole.
Rose quickly erased a two-shot deficit against Schauffele with four straight birdies on Sunday (NZ time) on an Aronimink course so soft from rain that tee times were pushed back three hours. That's something that I will look back on this week and think it was an incredible achievement. And he will face a possible penalty from the PGA Tour for failing to play enough events this year as part of its field enhancement criteria.
For Spieth, it's more than just missing the Tour Championship for the first time.
The top 30 on a season-long points list advance to the Tour Championship in Atlanta starting on Thursday week.