The 44-year-old became the oldest first-time winner in 18 years when he claimed victory by sinking a two-foot birdie putt after fellow American Stroud's long birdie try trickled just past the hole on the 18th green.
"Worked hard," said Duke, who had been a runner-up three times on the tour. "I knocked on the door a lot and here we are."
Both players parred the 18th in the first hole of sudden-death before returning to the 18th tee for what turned out to be the decider at the TPC River Highlands course.
Duke became the oldest first-time winner on the tour since Ed Dougherty, who was 47 when he won the 1995 Deposit Guaranty Classic.
Stroud forced the playoff by chipping in from across the green for birdie after sending his approach shot long after blasting a drive of some 340 yards.
"I'm glad I gave myself a chance in the playoffs," said Stroud, who was also chasing his maiden victory. "I wish that I would've won. Obviously, we all want to win. I gave it everything I had."
Duke fired a final-round of four-under-par 66 and Stroud posted 67 to tie on 12-under-par 268.
Graham DeLaet of Canada finished one stroke out of the playoff on 269 after shooting 69.
Another stroke back after a 70 was 2012 Masters champion Bubba Watson, who relinquished the lead to Duke with a triple-bogey six on the par-three 16th after finding the water fronting the green with his tee shot.
Watson, DeLaet and Charley Hoffman, who registered 72 for 272, entered the final round tied for the lead at 10 under par.
The leaderboard was jammed at the top for most of the day with a dozen players jockeying for position within two shots of the lead.
Duke took advantage of a lucky bounce at the par-four 10th, when he pulled his approach shot into the trees left of the green but the ball rattled around and bounced out onto the green to set up his five-foot birdie putt.
"I got an unbelievable break on 10," acknowledged Duke, who had only one top 10 this season from 18 starts - a tie for eighth at the Arnold Palmer Invitational.
"I knew it was going to be tough and that this guy wasn't going to give up. The main thing was, I didn't give up."
Watson, who won here in 2010, had trouble pinpointing his short irons but stayed ahead by making several par-saving putts.
He led by one shot coming to the 171-yard 16th but his tee ball landed on the bank and plopped into the lake. From the drop area, he flew his 125-yard shot through the green, hit a poor chip and two-putted for triple-bogey.
Duke, who turned professional in 1994, became emotional when asked about the improvements he had made since turning to swing coach Bob Toski for help.
"I wouldn't be here without him, no question. I talked to him this morning, and he said 'it's about time for you to win'," Duke said, breaking up. "And I did."
Final leaderboard top 20
Ken Duke (U.S.) 69 68 65 66
Chris Stroud (U.S.) 66 69 66 67
Graham DeLaet (Canada) 65 70 65 69
Bubba Watson (U.S.) 63 67 70 70
Webb Simpson (U.S.) 65 69 72 65
J.J. Henry (U.S.) 68 67 68 68
Ryan Moore (U.S.) 68 70 66 68
Charley Hoffman (U.S.) 61 73 66 72
Angel Cabrera (Argentina) 67 72 71 63
Stuart Appleby (Australia) 69 67 69 68
Morgan Hoffmann (U.S.) 68 71 66 68
Jeff Maggert (U.S.) 70 70 65 68
Rickie Fowler (U.S.) 72 68 70 64
Brendan Steele (U.S.) 68 68 72 66
Ricky Barnes (U.S.) 67 68 71 68
Russell Knox (Britain) 69 67 69 69
Justin Rose (Britain) 67 68 68 71
Kevin Sutherland (U.S.) 69 70 68 68
Keegan Bradley (U.S.) 69 65 72 69
Patrick Reed (U.S.) 66 66 73 70
- Sports & Recreation
- Bubba Watson