Durant's final total was 25-under 263. Matteson, the leader after Saturday's second round, finished at 21-under 267, tied with Lickliter.
The win was Durant's fourth on the PGA Tour, but his first since he won back-to-back starts in 2001 at the Bob Hope Classic and at Doral.
With the victory, Durant earned $828,000, the biggest check of his career.
Davis Love III, who won in Greensboro two weeks ago, double-bogeyed the closing hole to shoot 3-under 69 and fall into a tie for fifth with Vijay Singh (64), Nick Watney (68) and Marco Dawson (67) at 19-under 269.