Brown had two bogeys and six birdies, all within 10 feet. He is at 10-under 134 for the tournament.
"It was nothing too crazy," said Brown, who earned first PGA Tour win last season at the Puerto Rico Open. "I hit a few shots and made a few putts. It was just a good vibe day."
Kokrak, who opened with a 67 at Pebble Beach, had a 68 at Del Monte. Kokrak also had six birdies and two bogeys.
Morgan Hoffmann, who opened with a bogey-free 65 at Spyglass for a one-shot lead over four players, shot a 71 at Pebble Beach. Hoffmann had four bogeys and five birdies and is third at 136.
Starting on the back nine at Spyglass, Brown opened with two birdies and followed with two bogeys. He then had four birdies and no bogeys the rest of the round.
"I am really not doing anything differently," said Brown, now early in his third PGA Tour season. "I just feel a lot more comfortable out there then I did a few years ago. Not doing anything too crazy is good."
Hall of Famer Annika Sorenstam, who has played in the event several times since her LPGA retirement in 2008, had a 71 at Del Monte en route to a 141 total.
Gainey is grouped among seven players at par 144. Hadley carded a 73 at Spyglass and is grouped with seven players at 139. Potter, Jr., shot 71 and is tied with four other players at 137.
The 42nd event includes 80 professionals from the PGA, LPGA, Champions and Web.com Tours competing for the same prize money. The winner earns $60,000 of the $300,000 purse.