Watson, who won his first PGA Tour title at the event in 2010, recovered from letting a three-shot lead slip to edge Casey and secure a $1,152,000 payday.
The pair were level at 16-under after 72 holes and returned to the par-four 18th for a second time in search of a winner. Both players registered pars and so headed to the 18th tee once more. It was here that Watson triumphed, notching up a birdie while Casey stumbled, first finding the greenside bunker with his approach before firing his third shot into the gallery.
Watson had been forced to hold off a late charge by Casey, with the Englishman's round of 65 moving him into contention. The two-time Masters champion sat atop the leaderboard for most of the day despite not really getting going in a round of 67.
Back-to-back birdies at the opening two holes suggested that another low round was on the cards, but 10 consecutive pars followed as Watson struggled to find momentum. An eagle-three at the par-five 13th after holing a 39-foot putt gave him some breathing space, but a bogey on the 17th saw him drop down to the mark which clubhouse leader Casey had posted.
Watson had a 28-foot birdie putt at the last to win outright, but the American left it three feet short.
Casey's round of five-under 65 included three birdies in the last five holes after taking the turn in 32 courtesy of an eagle at the par-four third and a birdie at the eighth.
Overnight leader Brian Harman finished one stroke behind Watson and Casey after enduring an up and down final round of 69, which included four birdies and three bogeys.
Canada's Graham DeLaet finished in fourth, two shots off the pace, after shooting a closing 69.