Co-leader overnight with Argentine Gomez, Brown closed with a two-under-par 70 for a 20-under total of 268 at the Trump International Golf Club to claim a spot at this year's PGA Championship.
Brown, who had tied for fifth here 12 months ago in his rookie season on the PGA Tour, also earned a winner's cheque for $630,000 (£422,000) and a two-year exemption on the U.S. circuit.
Gomez, who like Brown had been bidding for his first victory on the PGA Tour, led by a shot playing the par-five last but fell back into a tie for second with his late bogey as he signed off with a 71.
The Argentine finished at 19 under par, level with American Jordan Spieth who fired a six-birdie 67.
Americans Justin Bolli (66) and Brian Stuard (68) were a further stroke back in a share of fourth place.