Stallings also held his nerve with clutch putts for par at the 15th and 17th on the challenging South Course at Torrey Pines before two-putting for birdie at the par-five last for a four-under-par 68 and a nine-under total of 279.
"It's pretty cool," Stallings, 28, told CBS Sports after mixing seven birdies with three bogeys to earn the winner's cheque for $1.098 million. "It hasn't quite set in yet but it's nice to kind of hold up coming down the stretch.
"I drove it very poorly today. I hit some good ones coming down the stretch but hit a really bad drive at 17 and managed to make a really good par."
Stallings, who won his maiden PGA Tour title in a playoff for the 2011 Greenbrier Classic before adding a second at the 2012 True South Classic, sank par putts from 14 feet at the 15th and six feet at the 17th to remain on course for victory.
He set up his birdie at the 18th with a four-iron from 225 yards but watched as his ball landed on the front portion of the green before rolling back to the fringe, with a pond lurking below.
"I hit that four-iron as hard as I possibly could, and just tried to get it over the front (of the green). It barely stayed," Stallings said.
American Gary Woodland and Australian Marc Leishman, playing in the final group, had the chance to force a playoff over the last two holes but Woodland's title bid ended with a double-bogey on 17 and Leishman's when he failed to eagle 18.
Leishman's wedge from 100 yards ended up four feet from the cup and he settled for a birdie and a 71 to tie for second with compatriot Jason Day (68), South Korean K.J. Choi (66), Canada's Graham DeLaet (68) and American Pat Perez (70).
The long-hitting Woodland, who like Stallings had been seeking a third victory on the PGA Tour, covered his back nine in two-over to close with a 74 and finish joint 10th at six under.
Damp overnight and early morning conditions made the tough South Course a little more receptive to low scoring and Sunday's final round ended up as a birdie slugfest with 10 players holding at least a share of the lead.
By the time overnight pacesetter Woodland had reached the turn in the final group, 17 players were bunched within two shots at the top of a wildly fluctuating leaderboard.
A stroke in front after the third round, Woodland offset bogeys at the first and seventh with birdies at the second and ninth for an outward nine of even par to remain at eight under overall.
That left him in a four-way tie for the lead with Perez, Leishman and early starter Choi, who moments earlier had birdied the final hole for a 66.
Woodland did well to save par at the 10th and 11th, sinking tricky putts from 12 and nine feet, and also at the 12th, where he got up and down from a poor lie under overhanging branches beneath the right side of the green, to remain at eight under.
Stallings seized the outright lead at nine under by sinking a 10-foot birdie putt at the 14th before being joined by Woodland, who knocked in a six-footer for birdie at the par-five 13th.
Both Woodland, at 14, and Stallings, at 16, slipped back with bogeys and six players shared the lead before Stallings got back to nine under with his birdie at the last, then watched to see if he would be caught.
Woodland's title bid evaporated when he pulled his tee shot into a hazard at the 17th on the way to a double-bogey six and Stalling's victory was assured when Leishman failed to eagle the final hole.
The tournament's top draw cards were both absent from Sunday's final round, Phil Mickelson having withdrawn on Friday with muscle pain in his back and seven-times winner Tiger Woods failing to make the third-round cut after a 79 on Saturday.
Between them, the two Californians have won the Farmers Insurance Open on 10 occasions and always attract huge galleries at the picturesque coastal venue.