Playing on a one-year exemption he earned through the 2005 Nationwide Tour money list, Axley entered the final round with a four-shot lead after consecutive rounds of 63.
He looked steady as a frontrunner on Sunday until he scattered shots all over the 14th on the way to a double-bogey, snapping a 53-hole streak of par or better.
The left-handed rookie also bogeyed the 17th, but the late lapses only served to thin his winning margin.
Axley closed with a birdie at 18 and shot a 1-over 71, finishing at 15-under-par 265 for his first victory in 27 career PGA TOUR starts.
'It got a little shaky there, but I held it together,' said Axley, who was calm during a television interview afterward, like a seasoned pro.
Anthony Kim, making his first PGA TOUR start on a sponsor's exemption, fired a 5-under 65 to move into a tie for second place with Dean Wilson (69) and Justin Rose (68).
Kim chipped in for birdie on the 17th, his eighth birdie of the day. Wilson was Axley's closest challenger for much of the day, but was done in by a bogey at the 15th. Rose collected his fourth straight top-15 finish.
None of them could catch Axley, whose only other professional win came on the Nationwide Tour last year.
Before his late-round miscues Sunday, when Axley missed shots this week he was only just missing them. But mostly he was making shots, finishing first in birdies, first in greens in regulation and ninth in putting.
It was a surprising performance for someone with little PGA TOUR experience prior to this season.
Axley, 32, missed the cut at the 2004 U.S. Open, his first PGA TOUR tournament, then missed 1-of-2 PGA TOUR cuts last year while playing full-time on the Nationwide Tour.
This year, in his first full season on the PGA TOUR, Axley had made just 10 cuts in 23 previous starts. Before this weekend, his biggest check was for $24,300.
Sunday, his winner's check was for $720,000 -- almost 3 1/2 times what he had earned in all his previous PGA TOUR starts.
'It feels unbelievable,' said Axley.
The wind was up Sunday at LaCantera Golf Club, and so were the scores. But Axley's grip on the lead was only loosened a little towards the end.
He flirted with bogey for the first time since the first round, but drained a 10-foot par save at the second hole. Axley then made a curling, 30-foot birdie putt at the fourth to get to 17 under.
Axley made another nice par save at the ninth, rolling in a 14-foot putt to keep his bogey-free streak alive. He then two-putted for par at the 10th, a hole that gave the rest of the field fits Sunday.
By then, Axley was six shots ahead of Wilson with eight holes to play.
Then, the 14th happened.
Axley was in the trees, in the fairway and in the rough twice on the way to his bogey seven.
'The first 13 holes I stuck to my game plan pretty well and was playing pretty conservative. But it slipped away from me at 14,' he said.
At the 17th, Axley missed a long par putt from the fringe and dropped another shot. But at the 18th, he knocked his approach within 4 feet to set up the closing birdie.
Someone in the gallery sounded an awkward scream when Axley's final approach landed close. It may have been his wife, Cortney, who leapt into her husband's arms before he could give a television interview.
'I'm so proud of you,' she told him. And if he was more excited than his wife, it sure didn't show.