The 33-year-old began the day in 11th place but moved through the pack as he carded a round of four-under 66, which moved him to nine-under for the tournament.
However, Dufner matched his achievement on the day, leading to the playoff in Texas.
Both players hit pars on the first hole of the playoff at the 18th and a solid putt from distance from Scott on the 17th kept his hopes of the title alive, as he matched Dufner's birdie.
On the third hole of the playoff, Dufner missed his putt allowing Scott to hole his seven-footer to win the event.
The Australian replaced Tiger Woods as world number one last week.