Moore shrugged off the jet-lag caused by a 9,000-mile trip from Las Vegas to Malaysia to fire a nine-under-par 63 and lead by two shots from fellow American Keegan Bradley.
Spain's Sergio Garcia returned a flawless 66 to lie outright third with five players a shot further back. Scotland's Martin Laird carded a 68 courtesy of four birdies in succession from the 11th.
After carding rounds of 69-63-69-68 to finish ninth in the defence of his title in last week's Shriners Hospitals for Children Open, Moore recovered from a bogey on the first hole today with five birdies in six holes from the fourth.
The 30-year-old picked up five more shots on the back nine to overhaul former US PGA champion Bradley, who had earlier completed a flawless 65.
In contrast, Open champion Phil Mickelson struggled to a 71 that featured five birdies but two double bogeys, including one on the ninth - his final hole - after driving into the water.
"I can't remember swinging this bad in a long time," the left-hander said. "I'm not sure if the ball is going to go dead left or snap hook right. I can't find the centre of the clubface.
"I'm trying something different on every swing. It's way off right now. It's as far off as it's ever been. It's a frustrating time tee to green, but I'm putting okay."
Nicholas Thompson's bid for a unique family double got off to a solid start with a round of 69, three under par.
Thompson is looking to become the second member of his family to win at Kuala Lumpur Golf and Country Club in the space of a fortnight after his sister Lexi, 18, won the Sime Darby LPGA Malaysia earlier this month.
Lexi's win came on the venue's East Course and although the PGA Tour event is being contested on the West Course, a win for Nicholas would make it the first time that a brother and sister have won events in the same season.
Cathy Gerring (nee Kratzert) won three times on the LPGA Tour in 1990 while her brother Billy Kratzert won three times on the PGA Tour between 1977 and 1984. Jim Gallagher Jr won five PGA Tour events between 1990 and 1995 and his sister Jackie Gallagher won an LPGA event in 1999.