By Mark Lamport-Stokes
The 29-year-old Haas sank a curling 43-foot birdie putt at the second extra hole, the driveable par-four 10th, to seal victory in bright afternoon sunshine at Riviera Country Club.
The trio had finished the 72 regulation holes on seven-under-par 277, Haas closing with a two-under 69 while Mickelson and Bradley each birdied the par-four last for matching 71s.
Spaniard Sergio Garcia fired a best-of-the-week 64 that included two eagles to share fourth place at five-under with Americans Dustin Johnson (71) and Jimmy Walker (69), and Australian Jarrod Lyle (70).
(Reporting by Mark Lamport-Stokes; Editing by Ian Ransom)