Trahan, 25, went wire-to-wire for his first PGA TOUR win despite closing modestly with consecutive 1-under 71s.
Both golfers finished at 13-under-par 275 for the tournament, then headed to the par-5 18th, where they played each of their three sudden-death playoff holes.
Trahan, who only birdied the 18th once in four rounds, made it twice when he tapped in at the first playoff hole. Durant matched his birdie with a 6-foot putt.
Durant was at a disadvantage on the second extra hole when his approach landed 10 feet away. He made the putt, then watched Trahan sink a 6-footer for his matching birdie.
Both players were in prime position on the third playoff hole after hitting the fairway with their drives. But Durant's second sailed over the green, while Trahan found the surface with his approach.
Sixty feet away, Trahan lagged his putt within 5 feet. Durant made a nice play, chipping to the same distance.
But after Trahan made his birdie try, Durant missed to end a long day at Annandale Golf Club.
'D.J. played great. My hat's off to him,' said Durant. 'He hit the shots he needed to down the stretch, and then in the playoff he played fantastic. He made the putt when he needed to and I didn't.'
After missing a chance to win outright with a birdie at the 72nd hole, Trahan birdied the 18th three times in a row for the victory.
'That was pretty sweet,' he said.
Trahan's win was his first in two PGA TOUR seasons. A member of Clemson's 2003 NCAA title team, his other professional victory came two years ago on the Nationwide Tour.
Sunday, Trahan had an eagle, a birdie and two bogeys. His eagle came at the par-5 fifth hole, but he followed it with a bogey at the sixth when he missed an 8-foot par putt.
Saving his round was a birdie at the par-4 14th -- a hole he had double-bogeyed in the third round.
'It was just a complete grind out there today,' said Trahan. 'I hung in there, and I'm proud of that. And I'm glad to be sitting here.'
Durant was looking for his fourth PGA TOUR title and first in five years. He had eight birdies in the final round, including two in his last three holes to join Trahan at 13 under.
He sat for a while as Trahan finished his round, but Durant said that didn't affect him.
'I was loose. I was ready to go,' he said.
Two-time U.S. Open champion Lee Janzen shot a 2-under 70 and finished in third place at 12-under 276. J.P. Hayes was one shot further back in fourth after his third consecutive 4-under 68.
Glen Day (66), Ted Purdy (68) and Bo Van Pelt (69) tied for fifth place at 10-under 278.