The 23-year-old fired a flawless seven-under-par 63 in warm, windy conditions at Waialae Country Club in Honolulu to post a tournament low of 14-under 126 after the first two rounds.
Five players shared the previous 36-hole record of 128 at the Sony Open, with John Cook the most recent in 2002.
Henley's playing partner and fellow rookie Scott Langley, the first-round leader, birdied his last three holes for a 66 to share second place with long-hitting Scott Piercy (64).
United States Ryder Cup player Matt Kuchar was at 11 under after shooting a 63, with compatriots Chris Kirk (62) and Charles Howell III (64), plus South African Tim Clark (66), a further stroke adrift.
Most eyes, however, were firmly fixed on Henley who had made only two previous starts on the U.S. circuit but was already looking like an ice-cool tour veteran.
He reached every green in regulation while playing in the company of his college friend Langley and ended the day with seven birdies to take control of the PGA Tour's first full-field event of the season.
"I didn't make every putt that was close but I was hitting great putts, hitting them like I want to hit them, and some were falling," a beaming Henley told reporters. "So I'm happy about it.
"It's pretty surreal. I remember I got my card after the (feeder Web.com) Tour Championship. My family was there and it was just kind of like, 'Wow, I just got my PGA Tour card.' You hope eventually one day you'll make it out here."
Henley, who shared low amateur honors with Langley when they tied for 16th at the 2010 U.S. Open, said playing with his college friend for the first two rounds at Waialae had been an unexpected bonus.
"It's ridiculous," he added. "We've been having a lot of fun together out there. We just have a lot in common, and it's been a fun two days. I'm living the dream, doing what I want to do.
"Coming out here with not really any expectations, just trying to play my game... that mindset, it takes a little pressure off me, and playing with Scott helps, too.
Asked to outline his goals for the week, Henley replied: "I've never been in this situation, so I'm just going to try to hopefully have a good weekend, and whatever happens, learn from it and have a good rest of the year."
Dustin Johnson's bid to complete a rare victory sweep in Hawaii ended prematurely on Friday when he withdrew from the Sony Open because of flu after completing just nine holes in the second round.
The big-hitting American, who triumphed by three shots at the season-opening Hyundai Tournament of Champions at Kapalua on Tuesday, was three over for the round, and for the tournament, when he told officials he was pulling out.
Johnson had been aiming to emulate South African Ernie Els, who in 2003 became the first player to win the Sony Open and Tournament of Champions in the same season.
The cut fell at two-under 138 with defending champion Johnson Wagner and 2012 U.S. Ryder Cup captain Davis Love III among those missing out.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by John O'Brien)