With barely a breath of wind in the Nevada desert, Henry sank two lengthy putts to finish birdie-eagle at the TPC Summerlin and seize an early one-shot lead over Argentina's Andres Romero, who recorded two eagles.
Americans James Driscoll and Jonathan Byrd opened with 63s while Canada's Stephen Ames carded a 65 as most of the early starters dipped well under par at a PGA Tour event known for low scoring.
Henry, however, commanded the spotlight as he scorched his back nine in seven-under 28 after starting the round at the par-four 10th.
Having reached the turn in four under, he birdied the second, fourth, fifth, sixth and par-three eighth, where he rolled in a 20-footer, to get to nine under for the round.
He then signed off in style, draining a 55-foot putt for eagle from just off the green at the ninth before raising his putter in celebration.
"It was just kind of one of those days," Henry, a double winner on the PGA Tour who is playing in Las Vegas for the first time since 2009, told Golf Channel.
"The golf course was beautiful today - not much wind and the greens were pretty soft.
"It was nice to make that putt on my last hole for a little eagle and make lunch taste that much better."
Henry had set up the eagle putt by hitting a good drive followed by a hybrid club for his second shot which ended up just off the back left of the green.
"You are never really trying to make a 55, 60-foot putt but just trying to get it up there somewhere close and kick it in," said the 38-year-old, whose most recent PGA Tour victory came at the 2012 Reno-Tahoe Open.
"And sure enough it kind of just rolled right over the front edge of the hole. You know you have to shoot low at this tournament and get off to a good start like that. Hopefully I'll continue the momentum for the next three days."
American world number 11 Zach Johnson, the highest-ranked player in the field for the second event of the PGA Tour's 2013-14 season, opened with a 69 while double major winner Angel Cabrera of Argentina carded a 73.
Former U.S. Open champion Webb Simpson, multiple major winner Vijay Singh and in-form Canadian Graeme DeLaet were among the late starters.