The Dornoch man secured a $64,800 pay-day for his effort at The Abaco Club, where he shot rounds of 68, 66, 73 and 68 for a 13-under-par total.
It left him in second spot on his own, three shots behind Andrew Landry, the American who led after the opening round in last year’s US Open.
Gunn, who was in top spot after 36 holes, held the overnight lead entering the final day with 28 holes in front of him.
But he played the final 10 holes of his third round on Wednesday morning in four-over to drop two shots off the lead entering the final round.
The 36-year-old was then one-over through three holes but fought back with birdies at the fourth, sixth, eighth and ninth holes.
That burst earned a share of the lead before Landry ran away from everyone on the back nine.
Gunn reckoned that a change in the weather conditions had dented his hopes of a maiden victory on the PGA Tour’s development circuit.
“I like playing in the wind and, as soon as it went calm, I couldn’t play again,” he said.
“It was a good week. Just five bad holes killed me. You can’t do that when the wind goes down.”
The Scot has played on the Web.com Tour full-time in both 2014 and 2016, recording two top 10s in 43 starts.
Prior to this effort, his best finish had been a tie for sixth in last year’s Servientrega Championship.
His lone PGA Tour start came after qualifying for the 2015 US Open at Chambers Bay, where he recorded a top-30 finish.