The left-hander and fellow American Simpson both finished on 15-under par after final rounds of 69 and a second additional hole was needed to separate the pair.
A fine approach shot out of a fairway bunker enabled Watson, who turned professional in 2003, to find the cup with two putts and claim victory.
The U.S. duo finished two shots clear of compatriots Jason Dufner and Tommy Gainey and South Korea's K.J. Choi, who all ended the tournament on 13-under.
Watson, who had won earlier this year at the Farmers Insurance tournament at Torrey Pines, slipped three-strokes behind Simpson, 25, with only eight holes remaining of regulation play.
"This week, I won [by] not getting down on bad shots, just staying focused on what I'm supposed to be doing," Watson told the PGA Tour's official web site.
Simpson was hit with a crucial one-stroke penalty on the 15th hole when he was penalized after his ball moved on the green while he was contemplating his next shot.
"I better limit my comments on that rule, because I think it's such a bad rule," said Simpson.
"When the wind or other natural things affect the golf ball, the player shouldn't be penalized. ... It was just unfortunate, but Bubba deserves a win, and I'm pretty happy for him."
Watson sympathized with his opponent and acknowledged the punishment handed out to Simpson played a part in his victory.
"If I didn't win, he would have been a nice guy to have win. We went to a playoff, so obviously one shot is the difference. ... It's a sad way to win, but I won."
Australia's Matt Jones finished tied with American George McNeill on 12-under in sixth, with five players, including world number three Luke Donald, finishing one shot further back.
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