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.