Johnson, who played in the afternoon, was nearly flawless, with his only bogey the result of a three-putt.
"Today was the first time it's kind of felt, the golf swing, I was in control, like I was leading into the Masters," Johnson told reporters after switching back to an old putter.
"I've been saying it's close and I've seen signs of it. I hit a lot of really good shots, drove it well, did everything really well. It's the first time in a long time I've done that.
"Even the bogey I made I hit a great shot right in the middle of the green and just three-putted."
Johnson retains the world number one ranking even though his season stalled after he fell over and injured his back just before the Masters and was ruled out of the first major.
However, he had built such a big lead atop the rankings courtesy of three victories before the Masters that he remains on top despite a mid-season slump.
Henley, meanwhile, played conservatively and aimed for the centre of greens in a strong start in the first of the PGA Tour's four FedExCup playoff events.
"Greens were really smooth, so almost made a couple (of putts) early and rolled in a couple of five-footers and then just felt comfortable for the rest of the day," he said.
Henley, who won the Houston Open in April and made the cut in all four majors, led fellow American Johnson by one stroke, with Chris Kirk, Scott Brown and Colombian Camilo Villegas two behind. PGA Championship winner Justin Thomas eked out a 68.
"That was a really weird round of golf but just tried to stay patient the first nine holes," said Thomas, who bogeyed two of his first three holes.
"I had a really, really hard time getting focussed and getting into today.
"I just wasn't able to prepare as well as I would have, like last week just with everything going on and being tired."
British Open champion Jordan Spieth also made a decent start with a 69, but it was a different story for McIlroy and Matsuyama.
Defending FedExCup champion McIlroy shot 73, while world number two Matsuyama, who leads the FedEx standings, bogeyed four of his final six holes for 74.
(Reporting by Andrew Both in Cary, North Carolina, editing by Pritha Sarkar/Greg Stutchbury)
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