Schauffele started the final round five strokes behind overnight leader Woodland and fell further back with a bogey at the first at the Kapalua Plantation course on Maui.
But two eagles -- the second from 105 yards at the par-four 12th -- and eight birdies catapulted the American to his fourth victory on the PGA Tour.
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He finished at 23-under 269, while Woodland shot 68 for second place.
Rory McIlroy, who started the day in second, faded with a 72 to finish eight shots back tied for fourth.
A subdued Rory McIlroy said he would remain patient after another disappointing final round scuppered his chances of victory at the Sentry Tournament of Champions in Hawaii on Sunday.
The four-times major champion, playing for the first time on Maui, seemed ideally placed to put the heat on overnight leader Gary Woodland but once again failed to deliver in the final pairing, a one-under 72 the worst score of the top 10 finishers at Kapalua.
Xander Schauffele, who flew under the radar until an eagle at the ninth, slipped through for victory and his course record-equalling 62 was 10 strokes better than McIlroy's round.
"My attitude was much better today. I didn't press at all, I was very patient," McIlroy told reporters after finishing equal fourth on 15-under-par, eight strokes behind Schauffele.
"I obviously could have shot a better score, but I did what I wanted to do, gave myself plenty of chances, just couldn't get the ball to drop."
McIlroy, who has decided to focus on the PGA Tour this year, a decision which ruffled some feathers in Europe, has struggled to convert opportunities to victories.
He played the final round of the first major of 2018 with eventual winner Patrick Reed at the Masters but faded to finish equal fifth.
McIlroy was also paired in the final round last year with Tiger Woods (Tour Championship), Justin Thomas (WGC-Bridgestone Invitational) and Francesco Molinari (European Tour BMW PGA Championship).
He was beaten each time.
"It's just something I am going to have to persist with, keep putting myself in these situations," he said on Sunday.
"I don't think anyone could have lived with Xander today."
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