A hat-trick of birdies from the 15th gave 36-year-old Van Pelt a four under par 67 and on 16 under he moved one in front at the PGA Tour-sanctioned event.
Overton, joint overnight leader with Swede Fredrik Jacobson after a course record 62 at The Mines, was in control until he fluffed chips on the 14th and 15th.
The first produced his only bogey of the round and the second meant just a par on the driveable par four, but a closing birdie enabled him to sign for a 69.
Mark Wilson, another of the United States contingent in the 48-strong field chasing a first prize of $1.3million, was three behind Van Pelt in joint third place. Wilson also shot 67, but Jacobson managed only a level par 71.
Van Pelt, whose one PGA Tour victory came two years ago, actually began his day's work with back-to-back bogeys, but did not panic.
"I think it just comes from experience - I've been in this position before and have been playing this game a long time," he said.
"I just didn't make that big a deal out of it. There was a lot of golf left, I made two good swings on three and had an easy birdie there."
Three of his six birdies were tap-ins. He two-putted the third and 17th, both par fives, and found the green at the 292-yard 15th after hitting driver for the first time in the tournament.
Jacobson had four bogeys, but birdies on the 15th and 17th brought him back into things.
Malaysia's Danny Chia shares fifth with Fijian Vijay Singh and American Jason Dufner, but they have five strokes to make up.