The Aussie entered the final round four shots off the pace, but he quickly erased the deficit with three birdies through four holes, while Rahm played the same stretch at 3-over par.
Leishman threw it in cruise control for the remainder of the round, building a lead that grew to three strokes on the back nine. Rahm managed to make things interesting by playing the back nine at 5-under, but while attempting to force a playoff he left a lengthy eagle effort short on No. 18.
The victory at Torrey Pines marks Leishman's fifth PGA Tour title, and the second win an Australian has recorded on the Tour over the last three weeks. Cameron Smith won the Sony Open two weeks ago.
Rory McIlroy was three shots behind Rahm to begin the day, but he couldn't mount enough of a charge. Through four holes he was 3-over en route to a 3-under 69 on Sunday, finishing tied for third.
Here's the top of the leaderboard after the Farmers Insurance Open:
|Place||Player||To Par||R4 Score|
Tiger Woods recorded a 2-under 70 to finish tied for ninth, his best result at Torrey Pines since winning the event in 2013.