Johnson appeared to have secured a three-shot win over Dufner when he drained four-foot putt on the final hole. But he was penalized two strokes for failing to move his mark back after moving it out of Dufner's putting line.
That mishap reduced Johnson's margin of victory to one shot. The former Masters champion finished at 12-under-par 268.
Dufner claimed sole possession of second place at minus-11 with a round of 4-over 74.
He was coming off wins an April 26 win at New Orleans and last week's victory at the Byron Nelson.
Tommy Gainey (3-under 67) finished a distant third at minus-7 while Jim Furyk (68) claimed fourth one shot further back.
Celebrity Families of 2014 [PHOTOS]