The 23-year-old Vilips, in just his fourth PGA Tour start after turning pro last year, shot six-under 66 in Saturday's third round at Rio Grande's Grand Reserve Golf Club.
Vilips is 18 under for the tournament, one stroke clear of South African amateur Kieron Van Wyk and American Joseph Bramlett.
"I don't feel that surprised," Vilips said.
"I feel like my game has gotten a lot better over the years.
"Playing so much out of college and on the Korn Ferry and then just a lot of competitive golf, it just has sharpened me up a lot."
Vilips has taken the outright lead despite battling a stomach bug.
"Feeling pretty good with the position I'm in," Vilips said.
"I wish my stomach felt a little bit better but it is what it is. You've got one more day, just battle through it."
If he salutes on Sunday, Vilips will be just the 12th golfer since 1970 to win in one of his first four PGA Tour starts and the 37th Australian to win on the tour.
Vilips, who was born in Jakarta, Indonesia, and grew up in Perth, last month was selected by Tiger Woods to be an ambassador for the 15-time major winner's Sun Day Red clothing label.
Vilips, like Woods, attended Stanford University in California and last year won his fourth tournament as a pro on the secondary Korn Ferry Tour - he finished 19th in that tour's standings to get his PGA Tour card.
In Puerto Rico, Vilips' third round featured seven birdies and one bogey to follow shooting 65 and 67 in the initial two rounds.
The Australian is being chased by a pack featuring 23-year-old amateur Van Wyk, who is making his first PGA Tour start.
Van Wyk is seeking to become the second amateur winner in two years on the PGA Tour, following Nick Dunlop's victory last year at La Quinta.
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