Casey had overcome a three-stroke deficit with five to play, tying Watson at 16-under 264.
But Casey lost his chance at the title while playing the par-4 18th for the third time, when his third shot from a greenside bunker flew over the green and landed on the cart path.
Watson, meanwhile, hit his 160-yard approach just to the right of the hole.
Watson had a chance to win in regulation, but bogeyed the 17th, while Casey closed with three birdies on the final five holes, sandwiched around a bogey on 15.
Watson finished with a 67 at TPC River Highlands, and Casey shot 65.
Watson also won a playoff in the WGC-HSBC Champions in China in November at the start of the season. He won the Travelers in 2010 for his first PGA Tour title.
This was the sixth time since 2004 the tournament has been decided in a playoff.
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