Leading by four on the last hole, he was able to smile and chat to the TV cameras in the fairway before making his seventh birdie of the day to cap off the victory.
Woodland's blistering 61 matched Justin Thomas' course record from the second round in 2015.
Ryder Cup victor Paul Casey threw himself into the mix with a 65 to share the third spot with India's Shubhankar Sharma one shot behind.
Paul Casey and Shubhankar Sharma are just a shot behind the joint-leaders following rounds of 65 and 64 respectively, while Austin Cook and Bronson Burgoon - leader after the first round - are another stroke back. Defending champion Pat Perez closed with a birdie to shoot 69 and was nine strokes off the lead.
Pepperell, who has two wins and two runners-up finishes this season, shot an even-par 72 Sunday to conquer a strong field and tough weather conditions.
Woodland finished second to American compatriot Ryan Moore in Kuala Lumpur in 2013 and 2014. "Kind of got a little loose there on the back nine, maybe ran out of gas a little, but it was nice to finish up with a birdie and nice to get some momentum going into tomorrow", said the two-time CIMB Classic runner-up.
"Just that one bad shot on the second, but other than that I was hitting it pretty good", said the 22-year-old. It's nice to play the ball down this week.
Leishman protected his position at the top of the leaderboard overnight following a 67, which included an eagle at the third after finding a bunker in a fast start, to sit at 19 under.
An emotional Leishman, who made eight birdies, including a putt from almost 50 feet on the par-4 ninth, and a solitary bogey, said it felt "unbelievable" to win.
Leishman finally had a blemish with a bogey on 13, but he steadied at the par-four 16th, rolling in a delightful curling birdie putt from 15 feet.
"It'd been over a year since I'd won, " he said. "That was the longest putt I made".
With the victory, Leishman earned a prize purse of US$1.26 million.
South Africa's Louis Oosthuizen, who shot 7-under 65 on Saturday, shot 3-under 60 on Sunday to join the five-way tie for fifth at 20-under with Woodland, Thomas, American Charles Howell III and Abraham Ancer of Mexico.