CROMWELL, 28 Jun 2015 (AFP) - Watson, who led after the first two rounds, stuck his approach shot on the final hole to within seven feet, while Casey found the bunker on his first two shots then blasted a sand shot over the green to all but eliminate himself from contention.
"Casey played great. I watched him make birdie on 17 from 16 green, and you know, I hung on and that's what we've got to do sometimes to win," said Watson.
The 36-year-old Watson closed with a three-under 67 to become the fourth player this year to earn two tournament victories. Casey posted a five-under 65.
The left-handed American finished at 16-under 264 in a tie with England's Casey, who made a late charge by making birdie on three of his final five holes of regulation to get into the playoff.
Both players parred the first sudden death hole, sending them back to the 18th tee for the third straight time in the round played under a light drizzle.
Watson's drive landed in the middle of the fairway and then he hit a brilliant approach shot onto the green.
He eventually made the seven-foot birdie putt, but the final hole was more about what Casey didn't do right.
His tee shot landed in the sand on the right side of the fairway and then the second shot found the bunker again just off the green.
His next sand shot sailed completely across the green and into a pack of fans who were standing on a cement cart path.
Casey chipped onto the green but by that time it was too late, especially with Watson having three putts to win.
"The round was great, it really was," Casey said. "I thought it was probably a tall order for a chance at winning.
"Actually thought those guys right behind us would probably stretch it out and keep making birdies.
"I feel fortunate to have a chance. I just couldn't get in the fairway on 18. I struggled on 18 today for some reason, but all in all it's been a great week."
Third-round leader Brian Harman of the US, birdied the final two holes for a one-under 69. He ended alone in third at minus-15. Canada's Graham DeLaet also closed with a 69 to end in fourth at 14-under-par 266.
Carl Pettersson, of Sweden, posted a four-under 66 to grab fifth at minus-13, while Zach Johnson (69) was one back at 12-under 268.
Leading scores after Sunday's final round of the PGA Tour's Travelers Championship (USA unless noted, par 70, x-won in playoff):
264 - Paul Casey (ENG) 67-68-64-65, x-Bubba Watson 62-67-68-67
265 - Brian Harman 66-65-65-69
266 - Graham DeLaet (CAN) 67-66-64-69
267 - Carl Pettersson (SWE) 65-66-70-66
268 - Zach Johnson 65-70-64-69
269 - Luke Donald (ENG) 68-68-67-66, Mark Wilson 66-68-67-68, Bo Van Pelt 70-68-65-66
270 - Jason Gore 64-68-69-69, Ken Duke 69-68-67-66, Brandt Snedeker 68-68-63-71, Chris Stroud 65-67-68-70, Jon Curran 67-67-67-69
271 - Steven Bowditch (AUS) 68-68-69-66, Martin Laird (SCO) 70-67-67-67, Nicholas Thompson 66-67-70-68, Mark D. Anderson 67-71-65-68, Brendon Todd 67-70-67-67