The 22-year-old, who turned professional just seven months ago, covered his final nine holes in 30 strokes to card a seven-under 65 at Torrey Pines South Course and break clear of a crowded leaderboard.
Rahm finished at 13-under 275.
"It's amazing," a beaming Rahm told CBS Sports after becoming the youngest ever champion at Torrey Pines and emulating fellow Spaniards Seve Ballesteros, Jose Maria Olazabal and Sergio Garcia as a PGA Tour winner.
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"Just to get into that position (to win) is so hard and I am so blessed to be able to say that I did it on my third time having a chance to win, having just started my PGA Tour career."
Taiwan's Pan Cheng-tsung (70) and American Charles Howell III (68) tied for second on a see-sawing day when eight players held at least a share of the lead during the final round.
Rahm, who will jump into the top 50 in the world rankings after starting the week ranked 137th, was three shots behind heading into the final round.
He moved into a tie at the top when he drained an 18-foot eagle putt at the par-five 13th after hitting a superb second shot from a fairway bunker.
"That putt was a little bit of just lagging it up there and hoping that it kept the line," the Spaniard said. "I just aimed between the two spots that we were thinking of and thank god it went in."
Rahm edged a stroke in front when he sank a five-footer to birdie the par-four 17th and effectively secured the title with his spectacular eagle at the last.
"I was just focused on making putts and hitting the right shots," he said. "After that second shot on 13, I was able to execute it so good."
(Reporting by Mark Lamport-Stokes in St. Augustine, Florida; Editing by Andrew Both)
