Jones shot a seven-under-par 64 at Newport Beach Country Club in California to establish a one-shot edge over both Michael Allen and Sweden's Freddie Jacobson.
Germany's Alex Cejka, South African Ernie Els and Australian Steve Allan are tied for fourth at 66.
Fred Couples, England's Paul Broadhurst, Australia's Cameron Percy, Spain's Miguel Angel Jimenez, New Zealand's Steven Alker and Koreans Y.E. Yang, Charlie Wi and K.J. Choi share seventh place at 67.
Jones had a brief PGA Tour career 20 years but played mostly on the Japanese tour, where he won 15 times, and notably won the 2023 New Zealand Open.
He started his Friday round by birdieing five of his first six holes, on the back nine.
"A fantastic start," Jones said.
"My head was buzzing at that stage, I couldn't in my wildest dreams (have) imagined getting off to that start that I did, but I felt calm and I felt that I could have gone on with it, too."
After the turn, Jones sank a 30-foot eagle putt on the par-five No.3, then made his lone bogey of the day on the par-three No.4. He bounced back with another birdie at No.7.
"After playing Tucson a couple weeks ago, I feel that I can actually, you know, let it go out here," Jones said of getting started on the Champions circuit.
"My strength is my length and I feel that I can hit it and there's a little bit of space here if you do miss it.
"Having said that, the greens are firming up and it's important to be in the right spots around the green.
"I've had to think a little bit more than I have in the past just to get those numbers where I want to land the ball and where I want it to finish.
"There weren't too many bad shots out there. Very, very excited with the start."
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