The 20-year-old, reigning NCAA champion playing in his third PGA Tour event since turning professional, trailed fellow American Bryson DeChambeau by a shot after the latter’s eagle at the par-five 18th but matched the feat to claim a round of 65 and clinch victory.
Wolff completed the back nine in 31 to finish the tournament at TPC Twin Cities on 21 under par, having started the day in a three-way tie for the lead after a third-round 62.
DeChambeau’s closing 66 earned him a tie for second alongside Collin Morikawa, another rookie American, who had to settle for a birdie at the last as he too finished with a 66 including six birdies in his final eight holes.
Wolff had the edge after the front nine, having gone through in one under, a shot better than DeChambeau and two clear of Morikawa.
But it was level pegging again after 13 holes as Wolff birdied the 10th, DeChambeau the 10th and 13th and Morikawa the 11th, 12th and 13th.
Birdies on the 14th and 15th put Wolff back in the box seat, but he had to settle for pars on 16 and 17, while DeChambeau birdied 16 to trail by a shot and Morikawa birdied 15 and 16 to join his fellow rookie in the lead with one hole to play.
DeChambeau’s eagle catapulted him to the top of the leaderboard, but Wolff was not to be denied as he rolled in a 26-foot putt to move back in front.
Morikawa had the chance to force a play-off had he too made an eagle, but a birdie handed victory to Wolff.
Canada’s Adam Hadwin was fourth on 18 under after a 67, a shot ahead of Carlos Ortiz and Wyndham Clark.