Van Pelt ended the day with a 5-under 67, putting him 12-under and one stroke ahead of fellow American Jason Dufner.
Van Pelt trailed most of the day but got hot on the back nine with four birdies, including a long downhill putt on 18 that boosted him into the lead.
"I felt like I hit a pretty good second shot, just carried about 5 yards farther," said Van Pelt. "I was just trying to get the ball down there and 2-putt and get out of there, and lo and behold, it goes in the hole."
Dufner turned in an up-and-down 67 that included two bogeys and an eagle on the first five holes.
Friday's leader, Emiliano Grillo, slipped into third place with a 73 that included bogeys on two of his final three holes. He trailed Van Pelt by two shots heading into Sunday's final round.
Couple mistakenly served bag of cash at McDonald's drive-thru
Exploding whale video goes viral on Internet