Palmer, 46, and Hoffman, 45, had 10 birdies and three eagles in a format that produced low scores in the annual invitational pairs event during a break in the US PGA Tour schedule.
"We put ourself in great positions to make birdies," Hoffman said.
"I would say very low stress all day long. Ryan made some great putts. I was able to hit some good drives and be able to capitalize on pretty much all our shots."
Canada's Corey Conners and South Korean Lee Kyoung-hoon fired a 58 to share second with Americans Max Homa and Kevin Kisner.
The 12 duos will compete in a modified alternate shot format on Saturday and in four-ball in Sunday's final round at Tiburon in Naples, Florida.
"Tomorrow is a tougher format, but it sure helps to jump start when you can shoot a low one on the first round," Palmer said. "If we're both hitting it well, I think we'll have a lot of chances."
Two LPGA players are competing in the event, with world number two Nelly Korda and Denny McCarthy of the United States and Americans Lexi Thompson and Maverick McNealy both combining for 60s to stand in a pack sharing fourth.
