Schauffele, who came into the week on the back of victories in the Travelers Championship and JP McManus Pro-Am, took a two-shot lead into the final round and birdied the first two holes to immediately double his advantage.
What looked like a comfortable win proved anything but, though, the world number 11 dropping three shots in the space of four holes from the sixth to fall one behind fellow American Kurt Kitayama heading into the back nine.
Kitayama's bogey on the 17th dropped him back into a share of the lead and a closing par completed a superb 66 to set what looked a testing clubhouse target of six under par at the Renaissance Club.
However, Schauffele had regained his composure sufficiently to hole from 15 feet for birdie on the 14th and two-putt the par-five 16th for another to open up a two-shot cushion and a crucial par save on the 17th allowed the 28-year-old the luxury of a bogey on the last.
South Korea's Kim Joo-hyung had birdied the 16th and 17th to join Kitayama on six under but three-putted the 18th after running a long birdie attempt four feet past the hole and finished a shot behind in third.
England's Tommy Fleetwood and American Patrick Cantlay carded final rounds of 67 to share fourth place on four under, while Kitayama, Brandon Wu and Jamie Donaldson secured the three places on offer in the 150th Open at St Andrews for non-exempt players in the top 10.
Three-time major winner Jordan Spieth was within a shot of the lead when he birdied the 13th but followed that with a double bogey on the next and eventually signed for a 72 to finish in a tie for 10th.
"It's an incredible feeling," Schauffele said after the first event co-sanctioned by the PGA Tour and DP World Tour.
"It was a big sense of relief when that par putt went in on 17 and I could hit a couple of long irons on 18 and lag it up there.
"It was a very stressful day. Not going to put make-up on the pig here, it was a very average day. Probably my worst this week. Austin (his caddie) kept me calm.
"As boring as it is, you really can't get ahead of yourself in links golf. I was ahead, I was behind, I was ahead, I was behind. Just kept my head down and this is very rewarding. This is the first of many co-sanctioned events and it's an honour to win the first one."
The 20-year-old, Kim Joo-hyung who had never played a links course before this week, said: "I played really solid today.
"I played bogey-free until the last hole and 18 is one of the toughest holes we have this week and it was that last putt that just broke a little bit."
Jamie Donaldson, who carded a closing 67 to finished in a tie for sixth with Wu, US Open champion Matt Fitzpatrick and Cameron Tringale, said: "It's massive, although we have booked a holiday next week so the missus won't be happy.
"She can have a lovely holiday on her own!"