Moore leads by two from Keegan Bradley, with Sergio Garcia a further short back in third place.
Phil Mickelson struggled his way to an opening 71, however, the Open champion saying after his round that he has never swung the club so badly in his entire career as he is right now.
Moore shrugged off his 9,000 mile trip from Las Vegas, where he posted a top-10 finish in the Shriners Hospitals for Children Open, and produced 10 birdies in his blistering opening round, capped off in style with an approach shot to 12 inches at the last.
The other highlight of his round was the rare feat of picking up birdies on every par three.
“That might be the first time I've ever done that,” said Moore.
“I had four twos on my card. Especially these, I mean, because number 11 was playing about 230 or 235 yards, and I was hitting a five-wood in there, hit a great shot to about eight feet. I mean you don't expect that all the time, but it was nice..
“The last time I had a good round like this to start, I won the tournament," added the 31-year-old, whose opening 61 in the Shriners Hospitals for Children Open in Las Vegas last year earned him his second career title.
"You know, it's always great to get off to a good start and get comfortable on a golf course, especially one that you haven't played before, and to go hit it in the right places, put it in the fairway, putting it on the greens, and for me it was huge just to make some putts."
Mickelson was clearly bitterly frustrated with his efforts, despite his one-under-par 71 including five birdies and leaving him tied for 21st.
"I can't remember swinging this bad in a long time," he said. "It's way off right now. It's as far off as it's ever been… But I'm putting okay."