Couples birdied his final two holes to ensure the victory after taking a one shot lead over Hallberg to the 17th tee.
It was Couple's first appearance at the Senior Open Championship and his second Champions Tour major title after winning the Senior Players Championship in 2011
Hallberg, a three time winner of the PGA Tour and once a winner on the Champions Tour, recorded the equal best last round of 66 after a tournament best of 63 on Friday.
Overnight leader Bernhard Langer was still in front as he made the turn but a disastrous stretch of four holes through the middle of his back nine would cost him any chance. He double bogeyed the 12th then bogeyed the 14th, 15th and 16th holes and eventually finished in a share of 6th.
Peter Fowler finished as the leading Australian in a share of 6th but he will be shattered by his double bogey / bogey finish which essentially cost him third position.
Peter Senior was well positioned through 36 holes of the event but eventually finished 22nd.
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