Duke was in the clubhouse with a one-stroke lead at 12-under-par 268 after finishing a round of 4-under 66, but Stroud then birdied the 18th to complete a 3-under 67 performance and knot him atop the leaderboard at TPC River Highlands.
The pair then returned to No. 18, where Stroud came out of a bunker to match Duke with a save for par.
Back on the 18th again, Duke produced the shot of the match by putting his approach within 2 feet of the cup, and, after Stroud two-putted for par, drained a short birdie putt for the victory.
Grabbing sole possession of third place at minus-11 was Graham DeLaet (69), who carded a 1-under 69.
Third round co-leader Bubba Watson was done in by a triple-bogey on No. 16, stumbling to an even-par 70 to finish alone in fourth at minus-10.