Playing two groups ahead of Simpson in windy conditions on Sea Island's Seaside Course, Duncan birdied three of the last four holes in regulation for a 5-under 65. He two-putted the par-5 15th for a birdie, made a 6-footer on the par-3 17th and a 25-footer on the par-4 18th.
"I'm just so happy to be here playing, and to come out here and win is just unbelievable,'' Duncan said.
Simpson birdied 15 and 16 and closed with two pars, making a 5-footer on 18 to match Duncan at 19-under 263.
"It played really tough all day,'' Simpson said. "It was blowing it seemed like a solid 20 and gusts here and there, and the pins were tough. They did a good job of setup, but they didn't make it easy for us. It was especially hard starting out the way we did, so I played really well given the conditions.''
They played the 18th twice in the playoff, matching pars on the first extra hole.
"I was definitely nervous, yeah,'' Duncan said. "I've been working really hard on controlling my emotions and breathing and all that stuff, and it paid off down the stretch here, especially this playoff. I was just able to keep calm and trust what I was doing.''
Simpson has four top-seven finishes in eight starts in the event.
"I felt like it was going to go my way, but that's what great players do -- they birdie the last two holes like he did,'' Simpson said. "So, tough to finish that way, but all in all, a great week.''
The 30-year-old Duncan regained his PGA Tour card with a 12th-place finish in the Korn Ferry Tour Finals after finishing 163rd in the FedEx Cup standings. He shot a 61 on Friday, then made 18 pars in a 70 on Saturday that left him four strokes behind third-round leader Brendon Todd.
"I knew it was going to be a tough day out here,'' Duncan said. "It was colder, the wind picked up and I was just trying to do the best I could, fight until the end. I hit one of the best 4-irons I've ever hit on 17, 6 feet up the hill, and you guys saw the probably 30-footer I made here on 18 just to get to a playoff.''
He earned his first spots in the Masters and Tournament of Champions in Hawaii.
"Just so many different things that I'm very, very excited for,'' Duncan said.
Sebastian Munoz was a stroke back after a 68. The Colombian won the Sanderson Farms Championship in Mississippi in September for his first PGA Tour title.
"First maybe eight holes I was a little tight,'' Munoz said. "I was too careful with my speed. Then, I just kind of let it go and made a couple more putts and hit better shots and it was all good. I gave myself a chance on 18. It didn't happen this time, but it already did this year, so I'm happy.''
Todd, seeking his third straight PGA Tour victory, was fourth at 16 under after a 72. He took a two-stroke lead into the final round.
"I was definitely tired on the back nine,'' Todd said. "With no momentum going, no birdies through 14 holes, it just seemed like I couldn't summon the energy to make some birdies.
"I'm really appreciative of the last two wins that I just had in Bermuda and Mexico. Had another opportunity this week, but it didn't go my way. Just trying to keep getting in contention and closing out.''