After bogeying his first hole at the Plantation Course on Sunday, Schauffele - whose 62 tied the course record - proceeded to card eight birdies and two eagles, playing his last seven holes at 6-under to chase down Woodland and win at 23-under par.
The 25-year-old put on a ball-striking clinic down the stretch, holing out for eagle from 107 yards on the par-4 12th and hitting his final two approach shots from over 200 yards to within 12 feet.
Schauffele's triumph in Kapalua, Hawaii marks his fourth PGA Tour title in only 61 career starts.
Woodland did not go down without a fight, though. He entered the final round with a three-shot lead over the field (five over Schauffele) and posted a 5-under 68, missing a birdie putt on No. 18 that would have forced a playoff.
Schauffele and Woodland were the only two players in the field to birdie the difficult 17th on Sunday, adding to the drama at the year's first event.
Rory McIlroy, who was alone in second after the third round, shot a 72 to finish in a tie for fourth at 15-under in his debut at the Tournament of Champions.