Bryson DeChambeau set the target with a final hole eagle to post the clubhouse lead at 20-under-par, and in doing so he ultimately passed pressure on to youngsters Matthew Woolf and Colin Morikawa as approached the 18th one shot back.
Wolff was put under pressure by five-time Tour victor DeChambeau but he held his nerve to win on only his fourth Tour start at 21-under 263.
Matthew Wolff eagled the final hole to claim the 3M Open on Sunday and become the youngest victor on the PGA Tour since Jordan Spieth in 2013.
The 20-year-old golfer became just the third player to win the individual title at the NCAA Championship and a PGA Tour crown in the same year.
"I love this, I love being out here", Morikawa said.
But Wolff was not done as he sank the winning shot for a six-under 65 to win in only his third tour start as a professional at 21-under 263.
With the victory, Wolff is exempt on the PGA Tour through the 2021 season and will play in The Players, the Masters and the PGA Championship next year.
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She went 3-1 down with a terrible volley, but responded to lead 5-4 with two sizzling backhands that had the crowd erupting. He will next play either Sam Querrey or Tennys Sandgren in what will be his 39th appearance in a Grand Slam quarterfinal.
Morikawa birdied five of his first seven holes, but only three the rest of the way.
"These guys are really good, and I know I'm really good, so it's going to be fun", Wolff said. "A lot of my putts weren't going in today, and I was just kind of telling myself one's bound to drop in".
Canadian Adam Hadwin shot 67 to claim fourth at 18 under with Mexico's Carlos Ortiz (64) and Wyndham Clark (68) a stroke back. Six players rounded out the top 10 on -16, including Lucas Glover and Hideki Matsuyama.
After following two birdies with a bogey at the ninth, Wolff picked up shots at 10, 14 and 15 before his spectacular finish.
He made a 26-foot eagle putt at the final hole to secure his victory.
World number one Brooks Koepka was at three-under after a 72 to just make the cut but five-time major victor Phil Mickelson and last week's Rocket Mortgage Classic victor Nate Lashley were among whose tournament came to an early end.
It forced Morikawa to make his putt to force a playoff but his effort missed narrowly to the low side of the hole. And when he did that, I kind of told myself ... it would be pretty special to roll in an eagle and finish this deal off on 18.
Rafa Cabrera-Bello started the day a shot behind third-round leader Robert Rock but was in front by two strokes after making three birdies in his first five holes.