Price, who shot a 9-under 63 in the third round of the 1986 Masters, tied Calcavecchia with a 5-under 22 at the traditional event that is played the day before the first major championship of the year begins.
Both players parred the opening playoff hole, the eighth, and Calcavecchia then hit his tee shot at the ninth into Ike's Pond that fronts the green. After Price barely carried the water with his tee shot, leaving the ball on the front fringe about 15 feet from the hole, Calcavecchia again hit a ball into the water.
Calcavecchia conceded defeat, leaving Price with the first prize of a crystal goblet. No player has ever won the par-3 contest and gone on to win the Masters in the same year.
Alone in third place with a 4-under 23 was Jerry Pate. Although Pate has not played in the Masters since 1982, he takes part in the par-3 tournament by special invitation because of his status as a former U.S. Open champion.
Wednesday's event was also highlighted by back-to-back aces from Toshi Izawa. He holed his tee shot on both the fifth and sixth holes. But because he made a quadruple bogey at the fourth, he could manage only a 1-under 26.