Bradley, whose first PGA Tour victory came as a rookie at the Nelson two years ago, got even with a birdie at the 15th hole. But he missed a short birdie putt at the next hole to fall behind for good.
Charl Schwartzel, the 2011 Masters champ, shot a 68 to finish third at 10 under. His only bogey Sunday came at the closing hole, where he hit his approach into a bunker and then hit through the green.
Bae won $1.2 million, nearly matching his PGA Tour career earnings of $1.6 million in his 42 previous starts. His best finish on tour had been a tie for second last year after getting into a four-man playoff at the Transitions Championship.
Bradley had a couple of incredible par saves on the back nine before finally making his first birdie of the round, a 17-footer that had just enough to get into the cup at the 463-yard 15th hole. That gave him a share of the lead when Bae missed a par putt there from just inside 6 feet.
After Bae sank a 5-foot birdie at the par-5 16th hole, and was already walking to the next tee, Bradley had a shorter putt on the same line it horseshoed around the hole and didn't fall. The par put Bradley a stroke back with two holes to play, and he then hit his tee shot at the par-3 17th over the green and was unable to save par. That made it irrelevant that he finally had a par at No. 18, the hole he bogeyed the first three rounds.
When Bae hit his tee shot at the 17th green that is fronted by water, he watched anxiously and finally let out an obvious sigh of relief, bending his knees and leaning backward when the ball landed on the front edge of the green about 24 feet from the cup. He made the par, and Bradley was unable to scramble again.
Players wore red ribbons during the final round in memory of Ken Venturi, the 1964 U.S. Open champion and longtime CBS golf analyst who died Friday.
Justin Bolli shot a bogey-free 65 for the best round of the day and matched his career-best finish of fourth. A stroke further back at 272 were Morgan Hoffmann (66), Martin Kaymer (68) and Scott Piercy (72).
Tom Gillis, making his 150th PGA Tour start since 1993 and still without a win, started the final round only two strokes out of the lead. But he was already 6-over for his final round after a triple-bogey 7 at the sixth hole. He went on to a 76 and finished tied for 12th.
At No. 14, Bradley drove into the left rough between some trees and missed the green before chipping to 5 feet to save par. On the par 3 just before that, his tee shot settled behind the green, but he hit from there to 8 feet and made that putt as well.
After Bradley's opening drive of the day landed in rough near a temporary lemonade stand, he hit over trees and a bunker to 15 feet and save par at the hole he bogeyed each of the first two rounds. His tee shot at the 202-yard second hole went into a bunker, but he made a 6-foot par putt.
Bae's long putt off the back edge of that par-3 green slid just past the cup, causing him to step back and turn around in disbelief. He knocked in a 4-footer that circled the cup before falling.
The lead swapped at the downwind, 502-yard third hole when Bradley's drive went left into the water. He bogeyed while Bae rolled in a 27-foot birdie putt and responded with a double fist pump.
Bae built his lead to four strokes with three consecutive birdies, getting to 16 under when he two-putted from 33 feet at the par-5 seventh.
One of Bae's biggest reactions came after he made his par-saving 11-foot putt at the 462-yard eighth hole, where he drove into a fairway bunker and then had to hit back into the fairway before his approach shot.
- AP