Trahan shot a 7-under 65 to overtake Justin Leonard, who ended up in second place three strokes back.
The win, which earned Trahan $918,000, was his second on the PGA Tour.
"I knew I was going to have to go out and play some good golf," Trahan said. "A 65 was a good round. It was able to get the job done for me. I'm very happy."
Leonard, who led entering the final round, slipped to an even-par 72 and a total of 23-under 337.
Trahan had previously won the Southern Farm Bureau Classic in 2006.