The 32-year-old Tennessee native finished with a 15-under 265 total to earn $720,000 after playing almost flawless golf for most of the tournament.
Three players were tied for second place three shots adrift, Anthony Kim, Dean Wilson and Briton Justin Rose.
Axley enjoyed a stretch of 53 holes without a bogey or worse at the LaCantera Golf Club before he double-bogeyed the 14th hole.
But Axley had a big enough lead to survive a few jitters down the stretch and lift his season's earnings to over $900,000.
The left-hander had never previously finished higher than tied for 24th on the PGA Tour, although he did win an event on the Nationwide Tour in 2005.
Axley, who shot 63 in his second and third rounds, clinched victory with a birdie on the final hole.
Kim, playing his first PGA Tour event with a sponsor's exemption, fired a final-round 65, Rose carded a 68 to continue his fine recent form and Wilson a 69.