The 27-year-old vaulted to the top of the leaderboard with a 62 on Saturday but struggled to find his rhythm on the final day, allowing rivals to close up and pile on the pressure.
At one point there during the final hour there was a three-way tie with Webb Simpson and Kevin Streelman moving level.
But Martin held his nerve and the eagle on the par five 16th gave him the cushion he needed, with his eventual winning margin two shots courtesy of a birdie on the 18th which saw him sign for a three-under 68.
Streelman, who had birdied five of the final seven holes, settled for second after a round of 65.
But Simpson, who had also eagled the 16th to join the party at the top of the standings, slumped to fourth place after a bogey on the 18th.
That left Scotland’s Russell Knox, second overnight, in third after a round of 70 – his worst of the tournament coming as he struggled on the opening nine, with a double bogey on the ninth after bogeys on the third and eighth holes.
Martin, who turned professional in 2010, made the cut in this year’s PGA Championship.
Martin admitted he played a little too safely in the early stages of his final round but was relieved to pick up shots when it mattered on the final few holes.
“I tried to take the same mindset into today as I have had all week. I’ve been playing well all week,” he told www.pgatour.com.
“Playing with a little bit of a lead, a little bit of a cushion, I think I was more conservative just because I didn’t want to make any mistakes early and I never really hit it close and got much going.
“It was a tough course to have the lead at because you know that just hitting the middle of the green and making pars wasn’t going to get it done so to finish it off and finally get a couple of putts to go in there at the end was obviously huge.”