Pampling holed a 30-foot birdie putt on the final hole that clinched victory. He raised his right arm in the air as the ball still had another foot before it reached the cup. The 47-year-old Australian last won on the PGA Tour at Bay Hill in 2006.
Brooks Koepka closed with a 67 to finish second. Lucas Glover was tied for the lead with two holes to play until a bogey from the bunker on the 17th and a closing bogey for a 69.
Pampling returns to the Masters for the first time since 2007.