The 24-year-old Vilips fired a four-under 67 to climb 11 spots into a tie for sixth, just three strokes behind leader Aaron Rai.
Vilips, who opened with a 68, made a lightning start with birdies on the first two holes.
He then experienced a rollercoaster with two birdies and two bogeys from the seventh to the 10th, before gaining momentum on the back nine where he made four birdies and just one bogey.
Rai, like Vilips, made a 67 that gave him a one-shot lead over Presidents Cup captain Brandt Snedeker and Mark Hubbard.
Rai thought the Dunes Golf & Beach Club looked great on television when he watched Chris Gotterup win it two years ago, and he figured it would be a good place to play ahead of the PGA Championship next week.
He spent two days with Brooks Koepka, who shot 70 and was six shots behind, and has found the course to his liking.
"It's been a lovely environment to play in actually the first two days," Rai said. "I think being in a group with Brooks Koepka, Davis Thompson, who are both very good players ... obviously Brooks is one of the best players in the world. So it's created a great atmosphere to play in."
Rai, who has one PGA Tour victory, is at 10-under 132.
Snedeker, who will lead the Americans at Medinah in September, played bogey-free in a moderate breeze to post a 66. Hubbard shot 67 by overcoming some early mistakes to run off four straight birdies around the turn.
Koepka was trying to keep up with Rai until he went from the trees into a water hazard on the par-5 fifth hole and made bogey.
Myrtle Beach is an opposite-field event, but the winner still gets into the PGA Championship next week if he is not already eligible. Rai received a special invitation based on his world ranking. He is at No.42 in the world, the only player from the top 50 at Myrtle Beach.
That means nothing to him as he tries to win for the second time in three years.
"No matter what anyone's world ranking is, whether you are Scottie Scheffler, No.1, or a little lower down, there's no divine right in golf," Rai said.
"Everyone starts at the same playing field on Thursday, and everyone who is in this field is good enough to win. No one has any rights to walk in and play well and compete."
Ryan Ruffels, who opened with a 67, shot 70 on Friday. The Australian is tied 15th, five behind the lead.
Cam Davis beat the even-par cut by one with his 71.
The PGA Championship typically reserves a spot for the Ryder Cup captain, not the Presidents Cup captain, so Snedeker still has that carrot in front of him. And it helps that Myrtle Beach is not a course that favours the power players, especially for the 45-year-old Snedeker.
"This golf course sets up for me, so excited to be here with a chance on the weekend," Snedeker said. "This is what you work for, so kind of turn the brain off tomorrow and go have some fun."
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