Simpson, who won the Wyndham Championship two weeks ago, closed with a six- under 65, while Reavie posted a five-under 66 to end at 15-under-par 269.
The duo returned to the par-five 18th for the first extra hole. Both players knocked their second shots left of the green in thick rough.
Simpson pitched his third to 15 feet. Reavie hit a beautiful pitch shot inside three feet. Simpson, who birdied the 18th in regulation from a similar line, drained his birdie effort.
Reavie responded by knocking in his short birdie try as well.
They moved to the par-four 17th. After Simpson stuck his approach inside nine feet, Reavie pushed his out to the right, some 23 feet from the hole. Reavie's birdie effort missed right and he tapped in for par.
Simpson calmly drained his eight-footer for birdie and the victory. With the win, he also takes over the lead in the points race for the FedExCup.
"It was great. I told somebody that winning the second time might be easier, but it was certainly tough," Simpson said in a television interview after the win. "To finish the way I did, and birdie 17 in the playoff was awesome."
World No. 1 Luke Donald closed with a four-under 67 to join Jason Day (68) and Brandt Snedeker (66) in third place at 13-under-par 271. Day shared second at this event last year, while Snedeker tied for fifth a year ago.
Simpson and Donald played alongside each other in the fifth-to-last group and they put together spectacular front nines. Simpson birdied three of four holes from the second, while Donald converted three consecutive birdies from the third.
The duo matched eagles on the par-five seventh and birdies on No. 9. They made the turn tied for the lead at 15-under, but Donald fell off the pace with a double-bogey on the 12th and another bogey at 16.
Simpson tripped to a bogey on No. 10, then parred his next seven holes. As he was running off those pars, Reavie joined him atop the leaderboard.
Reavie, who birdied the second and fourth, caught fire on the back nine. He rolled in an eight-footer for birdie on the 11th, and came back with a 24-foot birdie putt at the 13th.
The 29-year-old Reavie grabbed the lead at 15-under with a 13-foot birdie effort on No. 14. He pushed his advantage to two strokes, when he poured in a 33-foot birdie try at 16.
The par-five closing hole proved to be Reavie's undoing. Simpson had converted a 26-foot putt for birdie on the 18th to get within one of Reavie.
"I thought in my head if I could shoot five- or six-under, I would be right there," Simpson said in a television interview before the playoff. "Chez has just played extraordinary golf on the back nine it looks like."
Reavie, who had to wait before teeing off on 18, found the first cut of rough with his tee ball. He laid up in the fairway, but blasted his third shot over the green. Reavie chipped to 11 feet, but his par-saving putt slid by the right edge and it was off to the playoff.
"I would hit a lob-wedge instead of a sand-wedge on my third shot," Reavie told the Golf Channel when asked if he would do anything different. "But, it is what it is. I just made one bad swing, and the wind switched just a little bit and carried it too far."
Watson, the third-round leader, drained a long eagle try on No. 18 to shoot three-over 74, which left him tied for 16th at minus-eigth.
While Reavie and Simpson were battling for the title, several others were fighting to remain in the PGA Tour playoffs for the FedExCup.
They were among the lucky ones who advanced. Among those who failed to stay alive in the playoff race were 2010 U.S. Open champion Graeme McDowell, J.J. Henry, Ben Crane, 2012 U.S. Ryder Cup captain Davis Love III and Padraig Harrington.
NOTES: Simpson collected $1.44 million for the win...This was the first playoff in the nine-year history of the tournament...The tour is off next week before returning to action in two weeks at the BMW Championship, where Dustin Johnson will defend his title.