Moore made a 5-foot birdie putt on par-5 18th hole after Woodland was short with his chip from just off the green.
Woodland and Moore finished regulation at 14-under 274 on Sunday with darkness descending on the Kuala Lumpur Golf and Country Club, forcing the playoff to be postponed until Monday morning. The players endured about 3½ hours of delays Sunday.
The tournament was an official PGA Tour event for the first time. Moore received a two-year PGA Tour exemption and a spot in the Masters Tournament.
The 30-year-old American won for the third time on the PGA Tour. He also won the 2009 Wyndham Championship and 2012 Shriners Hospitals for Children Open.
On Sunday, in a steady rain with shadows being cast by floodlights, Woodland had a chance to win on the 18th hole but missed a 10-foot birdie putt just wide by an inch.
Woodland settled for a 3-under 69, and Moore had 70.
Kiradech Aphibarnrat and Chris Stroud finished a stroke back.
The back nine Sunday was filled with suspense as the names atop the leaderboard kept shuffling back and forth.
Woodland, Moore and Kiradech made the turn with a share of the lead, but Woodland moved one clear with a 10-foot birdie putt on the 10th hole – his first outright lead of the tournament. He didn’t hold onto it for long, bogeying the 11th to move back into a tie.
Kiradech also had chances to move ahead with two birdie putts within six feet on the 11th and 12th holes that he missed by inches. On the next hole, a much longer birdie putt caught the outside edge of the hole and curled away.
Woodland birdied again on the 14th to go up a stroke before play was suspended by lightning for the second time.
When they returned to the course in a driving rain, however, Moore holed a 4-footer for birdie on the 16th to tie it up again and both players parred the rest of the way.