Having won the 2013 US Amateur Championship at the same course, Fitzpatrick was quietly fancied to complete the double, and he had given himself a great opportunity by starting Sunday at the top of the leaderboard with Zalatoris.
Fitzpatrick did not have it all his own way, missing a couple of relatively short par putts earlier in his round, but the Englishman produced the shot at his life on the final hole to set him up for a final-round 68.
During the first 11 holes, third birdies cancelled out as many bogeys, but a 45-foot putt on the 13th acted as the catalyst for a strong closing run.
A further lengthy birdie followed on 15 and although Fitzpatrick would end his round with three pars, the final one of those came as a result of a legacy-defining shot.
He overdid his draw off the tee, finding the fairway bunker and with seemingly little chance of taking on the approach, but forced to play to his left, he played a fade from 159 yards to within 15 feet.
It was a quite stunning shot which was followed by a tame effort for victory, similar to his putt on 17, and a par left Zalatoris with a chance to force a playoff.
The American, who has become a force at the majors, was closer to the hole than his direct rival, but his downhill putt grazed the left-hand side of the hole and went past, sparking scenes of jubilation in the Fitzpatrick camp.
Speaking on his miraculous shot on 18, he said: "Me and [caddie] Billy [Foster] spent quite a while talking about the 18th tee shot undecided.
"I hit the three wood into the bunker. If there's one shot I just did not want this year it's a fairway bunker shot. When I saw it leave the sand I couldn't be happier."
Earlier in the day, four birdies in his first six holes sent world number Scheffler to the top of the leaderboard, but bogeys at 10 and 11 left the American playing catch-up during the back nine.
A birdie on the last would have created a whole different dynamic for Fitzpatrick and Zalatoris who were in the group behind, but it was another strong showing from the Masters champion.
Defending champion Jon Rahm, who led the tournament after 17 holes on Saturday before a double bogey at the last, could only claim a tie for 12th position after a closing 74.