Walker, who started off the day with a four-stroke lead, kept Jordan Spieth at bay despite his late offensive to become the first two-time PGA Tour winner of the season.
The 36-year-old nailed five birdies and just missed out on a hat-trick of gains after his 10-foot putt on the final hole just rolled wide of the cup.
Spieth meanwhile started off by recording a birdie on the first hole, but his form went downhill fast as he carded three bogeys to plunge down the leaderboard. He would then fall further behind when he missed his putt on the 10th.
With his opportunity to catch up with Walker all but over, Spieth began to make an epic comeback as he nailed a 45-foot shot on the 14th and followed that up with a 10-foot birdie on the next hole.
However, he didn't stop there as he rolled in a birdie on the 16th and 17th after watching Walker do the same. Spieth ended his final round with an eight-foot par putt on the 18th hole, but his efforts were in vein.
Meanwhile, Billy Horschel finished in third place, his best finish of the year thus far, following a final round 71.
Daniel Summerhays and Chesson Hadley occupy fourth spot after hitting final rounds of 69 and 71 respectively.
Dustin Johnson recorded his second consecutive 68 to share sixth place with Ryan Palmer.