Bradley, who entered the final round three shots back of Rose, fired a 6-under 64 to get to 20-under for the tournament and force a playoff. He actually bogeyed his final hole to give Rose a chance of winning on the 18th.
Rose failed to capitalize on that chance, as he lipped out for par on his final hole. The Englishman had held a one-shot lead since Saturday but only shot 67 in the final round. However, Rose's second-place result moves him into No. 1 in the world golf rankings, taking over the spot from Dustin Johnson.
The playoff was a fitting end for the already lengthy event, as rained dumped on Aronimink Golf Club in Philadelphia, Pa., over the past few days, forcing revised tee times throughout the week and suspended play on Sunday.
Rory McIlroy (-18) played in the final group on Monday but only managed to card two birdies in a bogey-free round to finish alone in fifth.
Tiger Woods finished in a tie for sixth after shooting a 65 in Round 4. Woods advances to the Tour Championship for the first time since 2013.
The PGA Tour will take a week off before the season finale begins at East Lake Golf Club in Atlanta, Ga., on Sept. 20.