Rose, reigning Olympic champion and 2013 US Open victor, could have sealed victory with a par putt at the last regulation hole but missed narrowly.
Rose is the fourth Englishman to... He made that for par to finish the third round in sixth place, three shots out of the lead. If he doesn't qualify, Spieth would violate a recent policy requiring PGA Tour members to play a tournament they haven't been to in the last four years.
In an announcement video on Twitter, Finau said: "I'm so excited to be on the Ryder Cup team and I can't wait to get to Paris".
It was fantastic play even finished Monday after rain soaked the course overnight and pushed up tee times.
It had been more than six years since one-time golfing sensation Keegan Bradley had won a PGA Tour event.
Rose also heads to next week's season-ending Tour Championship in second place in the FedExCup standings, with a chance to overhaul Bryson DeChambeau and land a $10m bonus as FedExCup champion at East Lake in Atlanta.
"It's boyhood dreams, know what I mean?" He just had a short putt for a third-straight birdie to get to -16 and within one shot of the lead, but he pulled it a little bit left.
"But obviously it's a big consolation being World No 1".
Rose could have won in regulation but lipped out on the last hole to force the playoff.
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They will try again on Monday but with a similarly dire forecast and a saturated course that simply can not take any more punishment, there is every chance the event will be reduced to 54 holes.
Woods missed a 6-footer for birdie at the seventh hole but when he birdied the ninth, he turned in 31 and was just one stroke back of the leaders.
Such was the scoring at Aronimink that Woods had a 72-hole score of 263 for the sixth time of his career. "And I don't think that would have been good enough".
He put any doubts of him not being ready for the Ryder Cup to bed by firing off three straight rounds of 65 to start off the BMW Championship.
"I've played a few tournaments (this year) where I was close at the end", Woods said, whose missed opportunities to win this year include the Arnold Palmer Invitational, British Open and PGA Championship.
"I feel like I'm definitely a lot more rested and ready to go than most guys here, I'm sure", Fowler 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. "Nice to be back without pain". He joins eight other players in the last 20 years to win a major and a World Golf Championship and reach No. 1 in the world.