Competing for the third time in a PGA Tour event, Wilcox piled up seven birdies and a lone bogey to card a joint best-of-the-day six-under-par 64 in the third round at Waialae Country Club in Honolulu.
Birdies on the last two holes earned him an 11-under total of 199 and he will tee off in Sunday's final round a shot behind pacesetting American Chris Kirk.
"I felt pretty good coming down 18," Wilcox told Golf Channel after climbing from a share of 17th place overnight into a tie for second with compatriot Harris English.
"It's nice to play well here and make the first cut in a season that I get to play. Walking down 18, me and my caddie looked at each other and I was kind of having to pinch myself," said the 27-year-old from Birmingham, Alabama.
Wilcox secured his card for the 2013-14 PGA Tour via the lower-tier Web.com Tour last year, having won his first title on that circuit in April at the South Georgia Classic in Valdosta.
Three months later he became the fourth player on that tour to shoot a 59, dipping under 60 in the final round of the Utah Championship where he tied for third.
Asked how that experience compared with his impressive title bid so far as a PGA Tour rookie at the Sony Open, Wilcox replied: "The 59 was a special day.
"I had some family in town and the course was set up for me. But I feel like this one does too. I am playing on Bermuda (grass) again and feel like I am back home in Alabama.
"Both are special days but this is a dream come true to be able to play out here. It's pretty cool," smiled Wilcox, whose mother Kim is in her 13th year as the golf coach at the University of Alabama-Birmingham.
Wilcox, whose previous PGA Tour starts ended with missed cuts at the 2010 Canadian Open and 2011 U.S. Open, effectively launched his birdie surge on Saturday with an unexpected chip-in at the par-three seventh.
"It came out super-hot," Wilcox said of his chip from greenside rough. "Two days ago I could not hit that shot but I've been working really hard on the chipping green.
"It came out a little bit left, then it spun right and went in right in the middle. If it didn't hit the centre of the flag it was going to ricochet maybe eight, 10 feet but it went in."
Following that chip-in, Wilcox went on to record further birdies at the 10th, 12th and 13th, bogeyed the 15th, then picked up further shots at 17 and the par-five last to cap a very special day.
- Sports & Recreation
- PGA Tour
- Waialae Country Club