Gomez began the day in tie for the lead with Greg Owen, and with a plethora of players within striking distance.
Perhaps surprisingly it was the man ranked 290th in the world at the start of the week that made the big move on Sunday, with Gomez registering five birdies and a single bogey on his way to a first PGA Tour title in 70 attempts.
Owen's round of 70 saw him finish in second, four shots back on nine-under, while Phil Mickelson (65) climbed the leaderboard, claiming a share of third with Seung-Yul Noh (65), Michael Thompson (66), Matt Jones (68) and Brooks Kopeka (70).
Having birdied the third, an early bogey at the fifth saw Gomez briefly drop behind Owen, but a birdie at the eighth and a stumble from Owen at the ninth saw Gomez draw level once more.
A birdie at the par-three eleventh following a tee shot that landed within eight feet saw Gomez hit the front on eleven-under, and he moved further ahead with a birdie at the par-five 16th despite finding the sand, with a great wedge from the green-side bunker resting just two feet from the cup.
Having been forced to win his Tour card back on the Web.com Tour last year, the victory marked a welcome turnaround for the Argentinean, who becomes the first man from the South American country to win since Angel Cabrera triumphed at the 2014 Greenbrier Classic.
Owen too was searching for his first Tour title, but after a bright start to his final round, the Englishman faltered. Birdies at the third and seventh saw Owen snatch the lead from Gomez, but while his playing partner was picking up shots on the back nine, Owen was dropping them.
The 43-year-old left the 12th hole with a bogey five and a broken club after his frustrations got the better of him after finding the water from the tee. A further bogey followed at the 14th, and by the time Owen birdied the 15th, Gomez already had the title in the bag.
Mickelson will head to next week's U.S. Open still without a win in 2015, but feeling considerably better about his game after a round of 65. Eight birdies and three bogeys saw the American move up into a share of second.
It was the Jones who at times looked the most like catching Gomez, with the Australian moving to within two shots following four birdies in six holes from the eighth to the 13th. However, after failing to sink a 10-foot birdie putt on the 14th, Jones bogeyed the 15th to see his charge falter.
Boo Weekley (65), Billy Horschel (65), Russell Knox (66) and Chad Campbell (68) ended the week on seven-under and a share of eighth.