"Yeah it has been a goal of mine all season to make it to the Tour Championships, so I'm pretty proud to pull it off", Smith said. "I've been to the top of the game".
Rose could have won in regulation, but his 16-foot par putt on the final hole lipped out to force the playoff.
However, a steady round proved not enough around a soaked Aronimink, with McIlroy's two-under 68 bettered by Rose, who shot a three-under 67, and eventual victor Bradley, whose six-under 64 took him into a play-off with the Englishman.
The BMW Championship was the third of four FedExCup season-ending play-off events on the PGA Tour. "That's the thing with sudden-death play-offs, you make a mistake and it's all over".
He will have an unexpected week off before joining the American team for the September 28-30 Ryder Cup in Paris.
Woods booked his spot in the 30-man field at East Lake for the first time in five years after shooting a five-under 65 in the rain-delayed final round of the BMW Championship on Monday.
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.
Jordan Spieth's pockets could get a little lighter soon after he failed to qualify for the Tour Championship on Monday at the BMW Championship.
"I d love to go the Tour Championship winning because obviously I want to get to number one by winning golf tournaments, but today was fun", Rose said.
"A lot has happened to me over these six years", he added.
Tiger Woods, who celebrated his return to the United States Ryder Cup team by earning a share of the lead after the first round, was joint sixth alongside compatriot Webb Simpson on 17-under, while England's Tommy Fleetwood shared eighth place with Tony Finau, Rickie Fowler and Open champion Francesco Molinari.
All he won Monday at Aronimink was a designation that can't be taken away. Spieth started at 27th in the FedEx Cup standings and took a step backward, finishing with a 73 to tie for 55th.
Spieth would be the first player to violate the rule in its two years of existence.
Marc Leishman is the only other Australian to advance to the Tour Championship and although he is 29th on point he remains upbeat about his chances.