Mickelson used a pair of late birdies to finish at 15-under 269, a stroke ahead of Steve Stricker, who closed with a 67 but bogeyed the final hole at the Riviera Country Club.
The victory was the 35th on the PGA Tour for the 38-year-old Mickelson.
Mickelson, who won $1 million, needed birdies on the 16th and 17th holes and a 6-foot, par-saving putt on the 18th to beat Stricker, who finished ahead of him.
"It was an exciting finish. Obviously, I didn't want it to be that close. I felt like I got off to a good start and wasn't able to keep it going," Mickelson said. "But to fight through a round where I didn't have my best stuff and to make some key putts coming down the stretch and key shots, it feels terrific to pull off the victory."