Faxon fired a course-record-tying, 9-under 61 to end at 14-under-par 266. After a three-putt bogey on 16, Tjaart van der Walt birdied 17 and 18 to join Faxon at minus-14 and close a round of 6-under 64.
Faxon knocked his 7-iron approach to 3 feet. Van der Walt, not to be outdone, hit the flagstick with his pitching-wedge second shot. His ball came to rest 10 feet from the cup, but his birdie putt slid by the right edge.
The 44-year-old Faxon stepped up and rolled in his birdie putt for his eighth PGA Tour title.
'I got lucky and hit a great shot in pretty close, but Tjaart hit the flag after he birdied 17 and 18,' said Faxon, who collected $774,000 for the win. 'Then he hit a good putt, it just hung out there to the right and I wasn't going to take a whole lot of time on that putt of mine. I wanted to get it over with.'
For van der Walt, it was his first playoff on the PGA Tour. It was also his best finish of the season by far. Prior to this week, his best finish this year was a tie for 50th at the Buick Open in Michigan.
'I got beat. I gave it a good shot,' van der Walt said. 'I'm disappointed, but I'm not going to be hard on myself. I'll just keep trying.'
Third-round leader Justin Rose posted a 1-under 69 to end one shot back at 13-under-par 267.
Michael Putnam, who turned professional this week after receiving a sponsor's exemption into the tournament, fired a closing 7-under 63. He shared fourth place at minus-12 with former British Open champion Ben Curtis and Jerry Kelly.
Faxon got into red figures with a birdie on the par-4 second. He came back two holes later with his second birdie. After a pair of pars, the Rhode Island resident got to 8 under with a birdie on No. 7.
He made the turn at minus-9 thanks a birdie on the ninth. Faxon made it two straight as he birdied No. 10. He was not done either.
Faxon birdied the par-3 11th and made it four straight as his birdie try on the 12th found the bottom of the cup. After parring his next two holes, Faxon broke a four-way tie for the lead with a 4-foot birdie putt on the 15th.
He came right back with a birdie on the par-3 16th to briefly move two ahead. Faxon parred his final two holes, and watched as van der Walt played some stellar golf coming down the stretch.
Faxon, who made the cut on the number at even-par 140, became the first player to make the cut on the number and go on to win the tournament since Jose Maria Olazabal turned the trick at the Buick Invitational in California in 2002.
'It was a great round,' Faxon said. 'I hit the ball nicely from tee to green. I never made a putt the first two days. I was hitting all the corners and my caddy said you better aim at the edges because you're hitting them all. Everything went in the last two days.'
Van der Walt played the front nine in 3 under with birdies on one, four and nine. Around the turn, he picked up another birdie on the 10th to tie for the lead at minus-12.
After Faxon pulled one clear of the field, van der Walt ran home a 12-foot birdie putt on 14 to join Faxon at minus-13. The South African stumbled to a three-putt bogey on 16.
Van der Walt got that stroke back with a birdie on the 17th. The 28-year-old drained a 7-foot birdie putt on 18 to force the extra session.
'I'm very excited. I hit a good shot on 16, but I was misled by the pace of the putt on the first putt,' said van der Walt. 'Then I just stuck to what I've done all week.'
Kenny Perry closed with a 7-under 63 to end alone in seventh at 11-under-par 260. Corey Pavin was one stroke further back after a final-round 68. Woody Austin, the 2004 champion, shared ninth place with Darron Stiles and Nick Watney at 9-under-par 271.