Davis, an Englishman who's never won on the PGA Tour, used a birdie on the 72nd hole to force the extra hole. However, his approach rolled off the green of the lighthouse hole and into some rocks.
As Davis attempted to chip, his wedge moved a loose impediment. He quickly called for a rules official, who after checking the replay confirmed the penalty.
Davis conceded the tournament to Furyk before the world's sixth-ranked player putted out.
Furyk shot a 69 to finish at 13-under 271. The victory was his 15th PGA Tour win and second since March, earning him $1.026 million.