Ben Curtis had a 40ft putt then it blows 15ft off the green into the rough.
Kenny Perry, Boo Weekley, JB Holmes, Ben Curtis and Chad Campbell were the other American victors, while debutant Hunter Mahan halved with Paul Casey.
Masters champion Mike Weir lies second on level par, with Open champion Ben Curtis one over and USPGA winner Shaun Micheel two strokes back.
But the 29-year-old saw his four-shot overnight lead cut by one as American Ben Curtis fired six birdies in a six-under-par round of 64 to move second.
Playing with Irishman Padraig Harrington and former Open champion Ben Curtis, Montgomerie began in imperious fashion only to miss his 20ft birdie putt at the 1st by inches.
Bradley was delighted to have been named Rookie of the Year, having become the first player since Ben Curtis in 2003 to claim victory in his first major appearance.
Bradley's victory at the U.S. PGA Championship saw him join Ben Curtis and Francis Ouimet as only the third player in golf to have won on their major championship debut.
The first snake - named Ben after Ben Curtis, last weekend's surprise winner of the Open - was caught by a group of golfers who managed to get it into a box.
In the United States, American Ben Curtis claimed a two-shot lead at the halfway stage in the Texas Open after his second successive round of 67 on Friday at the PGA Tour event.
The Englishman was two shots behind a group of four tied for second, including last weekend's Quail Hollow winner Rickie Fowler, Texas Open champion Ben Curtis, 2007 Masters victor Zach Johnson and Scotland's Martin Laird.
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The American ended on 286 in a group including British Open runner-up Adam Scott of Australia, Masters champion Bubba Watson, 2010 U.S. Open champion Graeme McDowell and fellow former major winners Geoff Ogilvy and Ben Curtis.
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