Hale Irwin, who won this event last year, was five shots off the lead at 11-under-par 202. He was joined by John Jacobs and Jose Maria Canizares in a tie for third.
Davis held a two-shot lead to start the final round at Newport Beach Country Club and hit his second shot to five feet for a birdie at the second. He added a birdie at the third to reach 15-under but stumbled with a bogey at the fifth.
The Australian dropped another shot with a bogey at the eighth but he recovered nicely on the inward nine. Davis collected three birdies on the back side to shut the door on his challengers and earn a breakthrough victory.
Gil Morgan, who lost this event in a playoff in 2001, was joined by Bruce Lietzke in a tie for sixth at 10-under-par 203.
Jim Ahern, who held the lead after the opening round, was one shot further back at 9-under-par 204 along with Ed Dougherty, Hubert Green, Allen Doyle and Wayne Levi.