Martin punctuated the victory with a birdie at the final hole to card 68 and finish at 20-under-par 264 for his first PGA Tour victory in his 56th start.
Streelman, who had recorded five birdies in six holes to charge into contention, missed a six-foot birdie putt at the last, moments after Martin's eagle at the 16th, to finish with a 65 and on 18-under-par 266.
"I didn't hit it hard enough," Streelman said. "I had a left edge putt (but) it broke off on me."
Briton Russell Knox was third on 16-under.
"It was an awesome way to finish, four-under in the last four holes," Martin told Golf Channel after securing $1.08 million (671,201 pounds) and an invitation to next year's Masters.
"My heart was beating out of my chest (after the eagle). I'm glad I looked calm. I didn't feel like I had much going all day but that was huge."
Martin, the 2009 U.S. Amateur runner-up, had never led into the final round on tour, though he had finished third three times and was pleased to have continued his incremental improvement to finally clinch a title.
"I've always tried to get a little bit better every year and I think this is the next step," he said.
Streelman, meanwhile, could not quite emulate the charge he produced at the Travelers Championship in June, when he birdied the final seven holes to win, a PGA Tour record.
"It was kind of like the Travelers," he said of Sunday's round.
"I needed to make as many (birdies) as possible as quickly as possible, so I just kept attacking and hit some really good putts."
(Reporting By Andrew Both in Cary, North Carolina; Editing by Greg Stutchbury)
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