Moore, who made the gruelling trip to Malaysia after playing in Las Vegas last weekend, opened his round with a bogey before running off 10 birdies at the 78-man elite field tournament, co-sanctioned by the Asian Tour, to leave him thinking of a third Tour win.
"Obviously it's a great score. It's a great way to start a week," the 31-year-old told reporters.
"Really the last time I had a good round like this to start, I won the tournament. That was in Vegas last year," he added, referring to his victory at the Shriners Hospitals for Children Open.
"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."
Bradley enjoyed a welcome return to action after a two-week break by firing a bogey-free round, which was matched by European Ryder Cup winner Garcia.
South African Rory Sabbatini flew out of the blocks to reach the turn in six-under but could not match the fireworks on the way in, recording a bogey and eight pars to sit on five-under and level with American Boo Weekley tied for fourth.
British Open champion Mickelson was fighting his swing throughout his round and finished with a one-under 71 to sit tied 21st.
The big lefthander registered two double bogeys, one at the ninth when he hit his tee shirt into the water, and said only his putting saved him.
"I can't remember swinging this bad in a long time, and as I shoot video of my swing I'm doing everything wrong," Mickelson said after his opening round of the 2013-14 PGA Tour season.
"The path of the club is too inside, then it's vertical, the head's moving, my legs are loose. Divots are steep. It's terrible. This is the worst I've hit and I can't find the middle of the club face.
"And I'm not sure if the ball is going to go dead left or snap hook right and it's a frustrating time tee to green. But I'm putting okay."
Mickelson's playing partner, Asian Tour order of merit leader Kiradech Aphibarnrat, showed the five-times major winner how it is done by firing a round of 65 to lead the charge of the 10 Asian Tour players in the field.
It was a day to forget for big-hitting Bubba Watson, though, as the former Masters champion could only muster a six-over 78 to lie in 74th.
(Writing by Patrick Johnston; Editing by Peter Rutherford)
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