His first win was on the tour was wire-to-wire and came after a shaky 1-under-par 71 in the fourth round.
Durant qualified for the extra play with a 6-under 66.
Both players had overall scores of 13-under 275.
Trahan birdied the 18th three times in a row for the victory.
"That was pretty sweet," he admitted to reporters in a post-tournament media session. "It was just a complete grind out there today. I hung in there, and I'm proud of that. And I'm glad to be sitting here."
That trio had a score of 10-under 278.