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.
Wolff is the youngest first-time victor on the PGA Tour since Jordan Spieth won the 2013 John Deere Classic as a 19-year-old.
In just his fourth start on the PGA Tour, Wolff poured in an unlikely eagle putt on the 72nd hole to claim his maiden tour title by a single shot over Bryson DeChabmbeau and Colin Morikawa.
The reigning NCAA champion at Oklahoma State, Wolff also played in the Waste Management Open in February as an amateur, tying for 50th.
"I had no idea he was going to make that putt", DeChambeau said.
"My game was in great form, it just didn't show the first two days".
"I'm a 20-year-old and I'm saying, 'job security, ' but it really is", Wolff said. "I knew I had to put a good stroke on it and I hit a really good putt".
Reigning US college champion Wolff became the second-youngest US PGA victor in 80 years by firing a six-under par 65 in the final round to edge compatriots Bryson DeChambeau and Colin Morikawa by a stroke.
New Melania Trump statue in Slovenia gets mixed reviews
The first lady has become one of her home country's most famous exports ever since her husband became the U.S. president. The first lady's limbs are rendered stumpily and her facial features are undefined.
Yet this week, everything went in his favour, and now you can expect to see a lot more of the entertaining young star: His victory grants him a two-year exemption on Tour, and a spot at the Masters in 2020.
When his long-time friend Morikawa missed his own eagle chance to force a play-off, Wolff embraced his caddie Steve Lohmeyer and they cried.
Seeking his first tour win in 31 starts, Wyndham Clark, 25, shot a 64 and was tied with Adam Hadwin (69) one shot back. Six players rounded out the top 10 on -16, including Lucas Glover and Hideki Matsuyama.
Wolff, who made his professional debut two weeks ago by finishing 80th at the Travelers Championship and missed the cut at last week's Rocket Mortgage Classic, used stellar approach shots to help him record six straight birdies on Nos.
But Wolff hit his approach to the fringe of the final green before opting to putt his third shot, and the twenty footer dropped in off the flag stick to hand the youngster victory.
Brehm appeared to have it wrapped up with a two-shot lead playing the par-5 18th at the Peek'n Peak Resort.
DeChambeau produced a similar round, even through nine holes before making three birdies and an eagle on the back nine.
He'd begun the day in a three-way tie for the lead, but his brilliant 65 contained five birdies before it all came down to his final putt. "That's just something that I've got to work on".