The win was Durant's fourth on the PGA TOUR, but his first since he won back-to-back starts at the Bob Hope and at Doral in 2001. His first-place check of $828,000 vaulted him from 66th on the PGA Tour money list to 29th with a good chance of making it to the TOUR Championship in two weeks.
Matteson, who won the Frys.com Open in Las Vegas last week, only managed at 2-under 70 at the Magnolia course, but tied for second place with Frank Lickliter at minus-21.
Lickliter polished off a 10-under-par 62 hours before Durant's final putt found the bottom of the cup.
Justin Rose, who fired a 60 on Thursday at the Palm course, posted a 3-under 69 and took a solo fourth at 20-under-par 268.
Matteson wasted little time in building a two-shot lead with a 9-foot birdie putt at the first, but Durant would strike next. He birdied the third hole, then tapped in a short birdie putt at the par-5 fourth to tie for the lead.
It was Lickliter who assumed the top spot on the leaderboard thanks to an amazing, 10-birdie effort on Sunday. He knocked his approach to 3 feet to set up birdie at the 16th, then took the outright lead with a 22-foot birdie putt at the closing hole.
Lickliter was in the clubhouse at 21-under par, but Durant matched him there with a 6-foot birdie putt at the eighth. Matteson did not get anything going and parred his next eight holes after his opening birdie.
Durant was one ahead of Lickliter and Matteson, but both Durant and Matteson made birdie at the par-5 10th. Durant made a nice up-and-down from a bunker, while Matteson routinely two-putted for his birdie four.
At the par-3 12th, Durant kicked in a 3-footer for par. Matteson left himself with 44 feet for birdie, but missed that putt by almost 7 feet. He missed that putt and now found himself two behind.
At the driveable, par-4 13th, Durant laid up off the tee, but hit his approach inside 2 feet. Matteson blasted out of a greenside bunker to 8 feet and sank the birdie putt to stay two behind.
Durant birdied the par-5 14th and was three up on Matteson, but the dagger came in the form of a 15-foot birdie putt for Durant at 16. That put him four ahead, but Matteson moved out of the tie with Lickliter at 17 when his 4-footer fell into the cup.
There was little drama about the outcome as Durant reached the green safely in two. Matteson found a bunker with his second and could not save par, falling into a tie for second place.
Durant lagged his long birdie putt to tap-in range and did just that for the win.
Davis Love III, who won in Greensboro two weeks ago, threw away some cash on 18 Sunday. He double bogeyed the closing hole to shoot a 3-under 69 and fall into a tie for fifth place with Vijay Singh (64), Nick Watney (68) and Marco Dawson (67). The group finished at 19-under-par 269.
Jesper Parnevik (65), Jerry Kelly (68), Mark Calcavecchia (68), Heath Slocum (69) and Charles Howell III (70) tied for ninth place at 18-under-par 270.