Scheffler overcame an early stumble to card a closing 71 and finish 11 under par, five shots ahead of fellow Americans Bryson DeChambeau (70), Harris English (65) and Davis Riley (72).
The world No.1 is the 10th straight American winner of the PGA and joins the late Seve Ballesteros as the only players since 1906 to win each of their first three majors by three or more shots.
Rahm held a share of the lead with seven holes to play, but the former Masters and US Open winner dropped five shots over the last three holes to slump to a nine-way tie for eighth.
The Spaniard had wiped out a five-shot overnight deficit from Scheffler with a combination of three birdies in his first 11 holes and a front nine of 37, only to run out of steam - and a little luck - on the closing stretch.
Rahm, who had largely struggled in the game's biggest events since his shock move to LIV Golf, saw his birdie attempt on the 13th lip out before failing to take advantage of the driveable 14th after his tee shot took an unfortunate bounce into a greenside bunker.
Rahm then three-putted the 15th for par from just off the green and knew his challenge was likely over following a pulled drive on the next, the first hole of the so-called 'Green Mile'.
"That's f*****," Rahm exclaimed as the ball disappeared into the rough and he was soon proved right, the resulting bogey and Scheffler's birdie on the 14th giving the world No.1 some vital breathing space.
Scheffler also birdied the par-5 15th, two-putting from the same place where Rahm had taken three, before Rahm's tee shots on both the 17th and 18th found a watery grave.
Scheffler had taken a three-shot lead over Sweden's Alex Noren into the final round and found himself five clear after Noren dropped shots on the first and fourth.
Bogeys on the sixth and ninth allowed Rahm to move into a share of the lead on nine under par, but a birdie on the 10th gave Scheffler a lead he would not relinquish.
"I knew it was going to be a challenging day. Finishing off a major championship is always challenging," Scheffler said after being presented with the Wanamaker Trophy.
"I didn't have my best stuff ... but stepped it up on the back nine."
English's superb closing 65 had established a very early clubhouse target of six under par, although he had already boarded a 5pm flight by the time Scheffler's early stumble briefly threatened to necessitate a change of plans.
Adam Scott held a share of second down the stretch before dropping four shots in the last five holes in a round of 73 to ultimately finish tied for 19th.
Scott shared leading Australian honours at two under with Cam Davis, who closed with a 72.
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