That left Putnam at 12-under 130, a stroke in front of compatriots Shawn Stefani and Jason Bohn, who each carded 65s.
Fellow American Ken Duke was a further shot back at 10 under after firing a best-of-the-day 63.
Putnam, who made just one cut from his first three starts on the 2014-15 PGA Tour, was delighted to benefit from an early tee time as he piled up seven birdies in a bogey-free display.
“We teed off at 6:15 this morning and it was pretty calm,” the 2013 Web深圳桑拿网会所, Tour Player of the Year told Golf Channel.
“Actually the wind was opposite to what it usually is just because it was so early so we had some holes down wind and some pretty easy holes to start off.
“And then coming in, I made a few birdies and got it to seven under today. I’ve been working really hard on my game … and it’s coming into place. Hopefully I’ll have a good weekend.”
Stefani, like Putnam bidding for his first PGA Tour win, was in sharp form with his putter as he totalled seven birdies and a lone bogey.
“I’ve been hitting the ball really well for quite some time now,” said the 32-year-old, who also finished his round before the wind began to pick up in the afternoon.
“The last two days really have been credit to my putter. I kind of figured something out on Wednesday and I’ve just focused on that. I felt really comfortable on the greens and therefore I’ve made a lot of putts.”
The cut fell at three-under 139 with former major winners Angel Cabrera of Argentina, American Lucas Glover and Ireland’s Padraig Harrington among those failing to advance.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Gene Cherry)