The European Ryder Cup star banked a cheque for one million US Dollars (£624,000) as a result of finishing 17 under for the week, as well as ending a two-year wait since his last victory.
The 2010 US Open winner was two shots ahead of Bradley at the start of the day and ensured success with a strong back nine that earned him a four-under 68.
He was one under at the turn, having picked up a stroke at the par-five second, but strengthened his case on the back nine with four more birdies to balance against a solitary bogey-six at the 13th.
Bradley started strongly, with birdies at holes two and five but was level par for the front nine after giving back shots on eight and nine.
He finished three under for the round as he responded to McDowell's surge but it was not enough.
The pair were well ahead of the rest of the 18-man field, Bo Van Pelt finishing third four shots back from Bradley and seven adrift of McDowell.