But Duke made the better approach shot on the second extra hole, bouncing his ball in front of the flag and rolling it close.
"Yeah, it's been a long time," said Duke, who turned pro in 1994. "I've been on the Canadian tour, the mini tours, Asian Tour, South American Tour, all of them; Web.com, and it's just great to be a part of this big family on the PGA Tour."
Duke, who came in ranked 144th in the world, is the sixth golfer in eight years to get his first PGA Tour win here, joining J.J. Henry (2006), Hunter Mahan (2007), Bubba Watson (2010), Fredrik Jacobsen (2011) and Marc Leishman last year.
Canadian Graham DeLaet finished a stroke back in third place with a 269. Watson finished fourth, two shots behind, after making a six on the par-3 16th hole.
World No. 1 Inbee Park sank a 4-foot birdie putt on the first playoff hole against So Yeon Ryu, capping her final-round rally and winning the LPGA NW Arkansas Championship in Rogers, Ark.
In Glenview, Ill., Craig Stadler birdied four of the first six holes, then hung on to win the Encompass Championship by one stroke over Fred Couples by sinking a par-saving 12-foot putt on the final hole.
*-Ken Duke -12
Chris Stoud -12
Graham DeLaet -11
Bubba Watson -10
Webb Simpson -9
J.J. Henry -9
* - Wins on second hole of playoff