The 33-year-old Crane, an Oregon native who lives in Texas, finished with an overall score of 13-under 275 at Torrey Pines.
The victory was Crane's third on the PGA Tour and his first in nearly five years. He previously won the U.S. Bank Championship in 2005 and he BellSouth Classic in 2003.
Crane started the final round two shots off the lead but a couple of birdies moved him to the top of the leaderboard after three holes. He closed out the win with a two-putt par on the final hole.
Defending champion Nick Watney (68) tied with five other players for ninth place.
World No. 2 Phil Mickelson, caught up in a controversy over the type of wedge he used, shot a 1-over 73 and ended up in 19th place.