Rose looked on course for the tenth PGA Tour title of his career after American Bradley bogeyed the 18th following a wild tee shot.
Bradley topped Rose with a par on the first playoff hole to win the rain-plagued BMW Championship for his first PGA Tour victory in six years.
The 2011 PGA Championship victor had a hard time transitioning away from the anchored putting style and has seen quite a few lows over the past few years. He needed to make the Tour Championship field to get to 25.
"A lot has happened to me over these six years", Bradley said. Will he need to win a tournament, or is it enough that he's in the mix on final day after final day?
Despite fading with a final-round 69 to finish 15th, Hideki Matsuyama earned a spot in the season-ending Tour Championship after placing 27th in the FedEx Cup points race.
His joint sixth-place finish at Aronimink moved him to 20th in the FedExCup Playoffs standings, and comes just days after he was named as a wildcard pick by US Ryder Cup team captain Jim Furyk.
Rose could have won in regulation but lipped out on the last hole to force the playoff. I thought that thing was in the middle, but it wasn't to be.
Rose said it is an fantastic feeling to get to the number one rank. Second place receives $972,000 and third place receives $612,000.
"I've played a few tournaments where I came close at the end, but just didn't quite get the W", Woods said afterward.
"But that second round...you can't shoot over par here and that threw me so much". You're in all the majors.
"It's a game changer for a player like me that's not in the top 50 to get in the Tour Championship", he said.
The final round was played on Monday after persistent rain left the course unplayable on Sunday. He gets a trip to Maui to start next year for the winners-only Sentry Tournament of Champions.
Both McIlroy and Woods shot 62 on Thursday to jump out to the first-round lead at 8-under par.
Two other events have finished beyond the weekend, including Australia's Jason Day and Swede Alex Noren in a Monday playoff at Torrey Pines and American Troy Merritt winning July's Barbasol Championship in Kentucky on a Monday.
"To have a chance to win again this year, it s a very positive feeling".
"It's been a good stretch of golf". He fell out of the top 30 and will miss the Tour Championship for the first time.
Tiger will have a week off with the rest of the Tour, then the season finale begins on September 20.
As consolation prizes go, it was a pretty spectacular one, and just reward for his incredible consistency over the last 18 months.
"I'm glad it's over", Matsuyama said. But to put it all together, especially with the putter the way it was this week and the way it's becoming, is so gratifying.
"It's boyhood dreams, know what I mean?"