Vilips had been right in touch after opening rounds of 68 and 67, but on Sunday (AEST) mixed two birdies with a double bogey (on the par-4 sixth) to be nine shots off the lead.
Mark Hubbard birdied four of his last five holes for a 7-under 64, giving him a one-shot advantage as he goes for his first PGA Tour title and a chance to qualify for the PGA Championship next week.
Hubbard's late run of birdies, before he settled for a par on the closing hole at Dunes Golf and Beach Club, capped a day of low scoring with several players jockeying for the lead.
When it ended, eight players were within five shots of Hubbard, a group that included Brooks Koepka (64) and 45-year-old Presidents Cup captain Brandt Snedeker (67).
Hubbard was at 16-under 197, one shot ahead of Aaron Rai, who birdied four straight holes to start the back nine and closed with five successive pars for a 66.
This is Hubbard's 274th start on the PGA Tour. His best result was a runner-up finish in the Houston Open when it was held in the fall in 2019. More than any shot or putt, he has attributed his work this week mainly to a good attitude.
"I felt like I had some of the best ball control I've had all season, maybe my whole career today, but I felt like I was kind of leaving a few out there in the middle of the round," Hubbard said.
"I think Mark a couple of weeks ago would have gotten pretty frustrated and turned a 64 into a 68," he said. "I just stayed really patient and just tried and kept hitting good shot after good shot and eventually the putts started going in."
Koepka, with his best chance at winning since returning to the PGA Tour from LIV Golf, began the day out of the top 20 and at least gave himself a chance, five shots behind in a tie for eighth.
"If I can continue to do what I did today as far as ball-striking, which I feel like I've done over the past three months, it's just a matter of getting that putter heated up," Koepka said.
"I feel like I'm striking it as good as I ever have, driving it as good as I ever have. If I can continue to do that, then I'm going to be very pleased where I'm at for a while."
Koepka and Rai already are set for Aronimink next week and the second major of the year.
Ryan Ruffels and Cam Davis are the other Australians in the field at South Carolina.
Ruffels shot a third-round 72 and is in a tie for 43rd. Davis is three shots further back and in a tie for 70th at one-under for the tournament.