The 42-year-old Swede had a 14-under 126 total, the lowest 36-hole score on the PGA Tour this year and just a stroke off the tour record of 125 held by Tiger Woods, Mark Calcavecchia, Tom Lehman and Corey Pavin. Parnevik is seeking his first victory since taking the 2001 Honda Classic for his fifth tour title.
"What can I say?" Parnevik asked, shrugging. "I, of course, think the course has played very easy. It's always nice when you have a few to spare than the other way around. I would like to be in the lead by as many as possible."
Sweden's Mathias Gronberg was second after a 65 in dry, calm conditions at LaCantera Golf Club Resort Course. He eagled the par-5 14th with a 16-foot putt before birdies on 16 and 18 with putts inside 10 feet.
Two other Swedes - Fredrik Jacobson (65) and Richard S. Johnson (66) - were 9 under, and Justin Leonard, the 2000 and '01 winner, was 8 under after a 67.
Parnevik's Honda Classic victory more than six years ago came when he shared the first-round lead and never trailed the rest of the way. He had a wire-to-wire victory in the 1999 Greater Greensboro Open.
"He's probably a great front-runner," Johnson said. "I said to my caddie this morning, when (Parnevik) putts well, he putts really well. And, I mean, he always hits it good. He's going to shoot 4 or 5 under everyday if the weather is going to continue being like this."
John Daly shot his second 2-over 72 and missed the cut. It's the 14th time in 21 events this year that Daly has either missed the cut or withdrawn.