Starting on the back nine, Henry began slowly, with just one birdie in his opening five holes, but he approached the turn on four under before a blistering performance on the front nine.
The American birdied the second, fourth, five, sixth and eighth holes before sinking a long eagle putt from just off the green on the ninth to reach 11 under par.
"It was one of those days," Henry, who started his round at 7.42am local time, told the PGA Tour website. "There wasn't much wind and the greens were pretty soft. It was nice to make that putt on the last hole.
"I played solid on the front nine. It's still pretty cold in the morning. I was just trying to get my feet wet and shoot a couple under par."
Henry has never finished better than 46th in five previous visits and may need to make use of the momentum from his opening round, with the past three winners of the tournament having shot at least 20 under par.
The 38-year-old, a two-time PGA Tour winner, opened the season at the Frys.com open last week with a 16th-placed finish.
"Any time you start with the round I had, it gives you a lot of confidence for the rest of the week," added Henry.
Despite his heroics, Henry was just a single stroke ahead of Andres Romero, who had two eagles, including at the par-five ninth, in his flawless round on a low-scoring day at TPC Summerlin.
The Argentinian had an opportunity to match Henry's score but missed his 29-foot birdie putt on the final hole.
It was still Romero's career-low score by three shots and he said: "I was feeling very good this week, my swing was there, I was hitting the ball well and I had a really good round.
"I thought I was going to finish leader but unfortunately Henry had one more birdie."
American trio James Driscoll, Jonathan Byrd and Jeff Overton were all on eight under to be tied for third while 2012 US Open champion Webb Simpson was a shot further back.
Canada's Stephen Ames, John Senden of Australia and American quartet Bryce Molder, Scott Brown, Heath Slocum and Chesson Hadley finished on six under.
World number 11 Zach Johnson, who is a clear favourite this week, is nine shots off the lead.