Walker entered the final round with a six-stroke lead but saw it shrink with bogeys on the 10th, 12th and 13th holes.
Another bogey on the 17th narrowed his advantage over Dustin Johnson and Jim Renner to one stroke, but he saved his victory with a 5-foot par putt on the final hole to finish at 11-under 276.
It was Walker's third victory in eight starts in the wrap-around PGA season. He joined Tiger Woods, Phil Mickelson and David Duval as the only golfers since 1999 to win three events in eight or fewer starts.
Two-time winner Johnson nearly caught him with the low round of the day, a 6-under 66. He shared second at 10-under with Renner (67).
Knotted for fourth at 8-under 279 were Jordan Spieth (67) and Kevin Na (68).
Hunter Mahan (72) claimed sole possession of sixth at minus-7.