Price and Calcavecchia had a two-stroke advantage in the second round of the best-ball tournament, but Faxon and Player matched their 23-under 119 total with a birdie on the 36th and final hole of regulation.
In the playoff, Price made a birdie on the par-4 18th, while Faxon and Player both failed on birdie attempts. Faxon rolled a 35-foot birdie putt within two inches of the hole, before Price closed out the match.
Price and Calcavecchia split $210,000, while Faxon and Player left with $160,000. The teams of Tim Herron and Dudley Hart and Davis Love III and Jay Haas tied for third at 22-under 120.
The event at Rhode Island Country Club had a total purse of $1.1 million.
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