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.
He and Bradley finished on 20 under par after a rain-delayed final round and the 2011 US PGA champion required just one extra hole to seal victory.
He was steady throughout the cold and drizzly final round and had a one-stroke lead when he got to the 18th tee. "It was really kind of unusual because I don t normally look at leaderboards, but I looked all day and I felt so solid", Bradley said.
Bradley won with a par while Rose recorded another bogey.
"A lot of hard work I've done with my coach Grant (Field) is paying off at the right time of the season".
Speaking about his new ranking, he added: "That's obviously boyhood dream stuff, something I'm incredibly proud of".
He will have an unexpected week off before joining the American team for the September 28-30 Ryder Cup in Paris. I under-read the putt a little bit. "Hit a great putt in regulation to (try and) win it, but then it was a poor playoff putt from me".
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The effect was especially great among Republicans, as "those likely to purchase Nike goods dropped from 51 percent to 28 percent". Jerry Falwell, Jr., president of Liberty University, told USA Today they are looking at their relationship with Nike.
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Apple's new iPhones are expected to come with big upgrades over the current lot, but also carry higher price tags. The XC will probably cost about £599, which is £100 cheaper than last year's iPhone 8 .
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Gareth Southgate has said that England have only produced one World Class midfielder in the last half-a-century - Paul Gascoigne.
"No 2 is an incredible spot to be in, and it's a week where there are many scenarios in play", he said.
Rose got a lucky break in the playoff when his approach shot landed in a skybox but ricocheted back towards the hole and stopped just off the green.
Tiger Woods and Webb Simpson finished tied for sixth at 17-under.
Meanwhile, Justin Rose said he would have like to reach the number one position by winning the BMW Championship.
"I felt so calm out there today", he told the Golf Channel.
The impetus behind the rule is so that fields across the board on the PGA Tour will stay healthy and so that some of the weaker events would get to see their favorite stars and superstars at some point.
"I assume it will either be a fine or I m adding some events in the fall", Spieth said.