The overnight leader went into the final three holes trailing Streelman by a shot after a cautious final round almost saw the American surrender his title bid.
However, Martin produced a timely moment of magic to eagle the par five 16th and then added a birdie at the last to claim victory on 20-under, two strokes clear of his compatriot.
With a five-shot deficit, Streelman went into day four knowing that a big effort was needed in order to bridge that gap as he sank seven birdies en route to a round-of-65 - three better than Martin.
It was Russell Knox - who ended day three two shots off the pace - that posed most threat to Martin at the start of play.
However, a disastrous front-nine comprising of two bogeys and a double-bogey on the ninth derailed the Scot's bid as Knox finished third on 16-under.