Putnam is chasing only the second PGA Tour title of his career following his maiden win at the Barracuda Championship back in 2018, while Hammer and Higgs are both chasing their first wins on tour.
Putnam carded a second consecutive 65 to move to 12 under par for the tournament, good enough to share the lead with Higgs, whose 63 was equal to the lowest round of the day, and Hammer, who shared the lead overnight and held onto it courtesy of a 66.
"I did a very good job of being patient," said Higgs, who enjoyed his best-ever 36-hole total on tour. "That would be the goal for the next two days, stay patient, which always gets harder. The better you do, the harder it is."
This week's event is making use of multiple courses at Sea Island, with players competing for the first two rounds on the par-72 Plantation Course and par-70 Seaside course, before the last 36 holes are to be played on the Seaside layout.
Higgs and Hammer both made their gains on the Seaside course on Friday, while Putnam was playing the Plantation course.
"I pretty much played flawless golf," Putnam said. "It was extremely easy. I was hitting most fairways and most greens. Just kind of a weird bogey came on the last from the middle of the fairway.
"But it has been a very simple week for me so far."
Higgs had a hot putter to thank for his 63, as he sank two putts in excess of 25 feet and another of more than 15.
"I have very good touch and I feel like I read the greens really well," he said. "I'm seeing them well."
Another trio follows just a shot back in a tie for fourth - Americans Joel Dahmen, Beau Hossler and Sahith Theegala, while four more players lie just two shots back, including South Korea's Seung-Yul Noh, Englishman Callum Tarren and Sweden's David Lingmerth.