A stroke ahead entering the day, Schauffele finished with a two-under 68 at TPC River Highlands to beat fellow Americans Theegala and J.T. Poston by two strokes. The Olympic champion had a 19-under 261 total.
"My mind was telling me to hit a good drive and then use your sand wedge or lob wedge in there and make birdie," Schauffele said.
"To sit there and watch what happened was a bit of a shock, obviously. I really had to try and focus on the task at hand."
Theegala shot a 67 and Poston had a 64.
Schauffele won for the sixth time on the PGA Tour and the second this season after teaming with Patrick Cantlay to win the Zurich Classic of New Orleans in April.
Theegala was lurking near the top of the leaderboard all day and grabbed a share of the lead on 15, driving the green on the par-4 hole and making a four-foot birdie putt. He overtook Schauffele with an 11-footer for birdie on 17.
But Theegala hit his tee shot on 18 left and into the front lip of a fairway bunker and needed two tries to get out.
"Somehow my body just, I just straight bladed it," he said.
"I had room there. I don't know how it looked, but I had room there. Just didn't think I would let myself blade it. But I guess the moment was — and then from there it's, like, got to try and make 5 now."
His 12-foot bogey putt lipped out, and he fell to his knees in agony.
"I did everything I thought I had to do and it just happened to be everything bad culminated on one hole," he said.
"I did so much good."
Theegala was trying to become just the second rookie to win this season, joining Chad Ramey, who won in the Dominican Republic.
Amateur Michael Thorbjornsen finished fourth at 15 under after a 66.
The Stanford University star was looking to become the first amateur to win on the tour since Phil Mickelson it in 1991.
"I felt really good and comfortable out there, then near the end had a couple of hiccups, which happens sometimes," Thorbjornsen, who added that he plans to return to college in the fall, said.
"I don't think I was too nervous, just a couple of miss-executions."
Australia's Cam Davis shot a final-round four-over 74 to finish in a tie for 56th at two under.
Patrick Cantlay began the day just a stroke behind his good friend Schauffele. But last year's FedEx Cup champion, who had a combined four bogeys in the first three rounds, shot five of them on the front nine on Sunday.
He finished with a 76 and in a tie for 13th at 10 under while Rory McIlroy, who shot an opening-round 62, finished at nine under with a 67.
