Moore had to fight just to get in the playoff, hitting an awkward 60-yard wedge shot on the 18th hole Sunday that dropped within several feet of the hole and allowed him to salvage par.
He and Woodland finished at 14-under 274, with the playoff postponed until Monday because of fading light.
In the playoff, Moore hit a similarly well-placed approach with an 8-iron to the same green that stopped about 5 feet from the hole, setting up his winning putt.
"I had a great opportunity there on 18 with my third shot and it was just an absolute perfect number," he said. "It was coincidentally the exact shot I was working on on the range."
It was Moore's third PGA Tour title and came nearly a year after he won his second at the 2012 Shriners Hospitals for Children Open in Las Vegas.
"I've always enjoyed playing in the fall. I'm not sure why," he said. "It's actually kind of funny, I won a week before my son (Tucker) was born last year; I won a week after (his birthday) this year."
Woodland, who was also trying to win his third PGA Tour title, had a chance to end things as dusk was descending in a steady rain Sunday evening but he barely missed a 10-foot birdie putt on the 18th that would have given him the title.
The players had endured about 3½ hours of storm delays earlier in the day, which caused the playoff to be put off until the morning.
"Obviously, I'd like to make that putt," Woodland said. "I hit it where I wanted to, it just broke more. I can see it now, it was a little lighter out right now, I can see it broke a little more, but it is what it is."
He pulled his approach shot to the 18th green wide Monday, leaving himself a difficult chip shot from the rough that he couldn't hole for birdie.
Still, it's been a remarkable turnaround in form over the past few months for the American who has struggled with wrist injuries in recent years and a loss of form that had sent his world ranking plummeting to 268th this summer.
Woodland began making changes to his game last January when he started working with new swing coach Butch Harmon. He later switched to Harmon's son, Claude, hired a new short-game coach, Pat Goss, and then added a new psychology coach, Julie Elion.
The results finally started to come in August: Woodland won his second PGA Tour title at the Reno-Tahoe Open and followed that with a share of second at The Barclays a couple of weeks later.
"I put a lot of hard work in," he said. "It's been a process with the changes I've made, switching to Butch and his son, and it's finally starting to come together, which is nice. I put a lot of work in on the short game, a lot of work on the middle game, and we're starting to put it together now."
Moore is also hoping to build on the victory at the $7 million Malaysian tournament, which became an official PGA Tour event this year, awarding FedEx Cup points and a spot in the Masters.
Given how well he has played at this time of year, he's also glad the new wraparound season is starting in October.
"Now that it counts, now that it's a full FedEx Cup event and counts as a win on the PGA Tour, it does so much for you. To get a win this early in the season, it's just incredible, to be able to get some FedEx Cup points racked up," he said.