The 34-year-old Streelman shot a final round of four-under-par 67 to finish on 10-under, two strokes clear of his nearest rival at the tricky Copperhead layout at Innisbrook Resort.
Boo Weekley finished outright second after closing with a63, the best single round of the tournament, to catapult himself up the leaderboard.
Cameron Tringale was third at minus seven after carding a 66 while Justin Leonard, the 1997 British Open champion, finished tied for fourth at minus six with last year's winner, Englishman Luke Donald, and Australian lefthander Greg Chalmers.
Streelman, who spent years driving himself around the United States as a struggling player trying to make the big time, joined the PGA Tour in 2008. His previous best finish was third, which he had done three times.
He started the final day in a three-way tie for the lead with Leonard and George Coetzee after a flawless round of 65 on Saturday.
He birdied two of his first three holes on Sunday and did not drop a shot all day, adding two birdies to secure his maiden Tour win.
"That was really cool," he said in a greenside interview with NBC television.
"It just shows that if you follow your dreams anything is possible." (Reporting by Julian Linden in New York; Editing by Gene Cherry)