Jose Maria Canizares, who won this event in a playoff in 2001, was joined by David Eger in a tie for third at 10-under-par 132.
Davis was one shot off the lead to start the day at Newport Beach Country Club and picked up his first birdie at the par-5 3rd. The Australian then hit an 8-iron to five feet for a birdie at the 6th and drained a 12-footer for a birdie at the very next hole.
At the par-4 9th, Davis hit his approach from the left rough to 12 feet for a birdie to make the turn at minus-10.
Davis continued his fine play on the inward half. He ran home a 10-foot putt for a birdie at the 11th and dropped a 6-iron inside 15 feet for a birdie at the 13th. At the par-5 15th, Davis rolled in a five-foot putt for his seventh birdie of the day en route to a bogey-free round.
'I'm driving long enough to get it close in two on the par-5s,' said Davis. 'It's not a long course.'
Davis, a veteran of both the European and Australasian Tours, is seeking his first career victory on the Champions Tour.
'I'm quietly confident. I don't know if it's fate or whatever,' said Davis, who set a new 36-hole tournament record. 'I've won quite a few tournaments when I've been leading.'
Ahern, who was atop the leaderboard after round one, got his first birdie of the day at the par-5 third. He parred his next 10 holes before a pair of birdies starting at the par-4 14th and birdied the par-5 18th for a round of 67.
Defending champion Hale Irwin had a steady round of 66 to finish four shots off the lead at 9-under-par 133 along with John Jacobs. Wayne Levi and Larry Nelson were one shot further back at 8-under-par 134.
'I had a pretty good score,' said Irwin. 'Probably should have been better considering how I started. I don't like to be behind starting the last day, I'd rather be leading.'
Jerry McGee, Jim Thorpe and Bruce Lietzke finished tied for ninth at 7-under-par 135.
Last year's runner-up Allen Doyle was seven shots off the lead at 6-under-par 136 alongside Tom Wargo and Dave Stockton.