Jones began and ended his round with birdies as he posted a 12-under total of 130 to finish level with American left-hander and former Masters champion Bubba Watson, who fired a 66.
Another left-hander, Greg Chalmers of Australia, was a further two strokes back after carding a six-birdie 67, ending the day level with American Harris English, who also carded a 67.
Journeyman Jones, whose best PGA Tour finish after playing six full seasons on the U.S. circuit was a tie for second at last year's Greenbrier Classic, was delighted to have an early tee time for the second round.
"We definitely got the good side of the draw going off early," the 33-year-old from New South Wales told reporters after mixing seven birdies with a lone bogey. "It's cold and the ball isn't going as far."
Watson, co-leader overnight with South Korean Yang Yong-eun after opening with a 64, was also upbeat despite having dropped two shots in his last three holes.
"I feel like I should win on every golf course," said the slim American, who is bidding for his first victory on the PGA Tour since his major breakthrough at the 2012 Masters.
"Everything is clicking right now. I played really well last week, just didn't make the putts. This time I'm playing well and some of the putts are dropping."
Japan's Hideki Matsuyama had been just one stroke off the lead after 17 holes but bogeyed the par-four 18th after finding a bunker with his approach to card a 67 for a nine-under total.
Korean Yang and three-times Phoenix Open champion Phil Mickelson, who also attended Arizona State University, were both among the day's late starters.
Mickelson, who won last year's title with a record-tying 28-under total of 256, carded a level 71 on Thursday having recovering from back pain which forced him to withdraw after the second round of last week's Farmers Insurance Open.
The cut was projected to fall at one-under 141 with England former world number one Lee Westwood and former major winners Padraig Harrington of Ireland and South African Retief Goosen among those in danger of missing out.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Gene Cherry)
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