The American fired a four-under par 67 to stand on six-under 136 after 36 holes along with countrymen Kevin Streelman, Brendon Todd and Chandler Phillips plus Canada's Mackenzie Hughes.
Windy and rainy conditions helped create a leaderboard logjam at Innisbrook's Copperhead course in Palm Harbor, Florida, with eight others one stroke adrift on 137.
Sunset fell with 15 golfers were unable to complete the second round, which will be completed Saturday morning before the third round begins.
Leading those unfinished were Rico Hoey of the Philippines at 5-under through 16 holes.
Cink, who defeated Tom Watson in a playoff at Turnberry 15 years ago to capture his only major title, seeks his ninth PGA Tour title and his first since capturing his third Heritage crown in 2021.
"I started off pretty scrappy, trying to find my footing, and then I did. I finished very strong," Cink said. "You have to be long and accurate off the tee, smart with your decisions coming into the greens and hit really solid approaches.
"There's a reason that so many players rave about this course. It requires everything and so far this week I've done everything fairly well."
Cink began on the back nine and birdied three of his first five holes, putting approaches inside five feet at 10 and the par-5 14th and inches from the hole at 12.
After missing the green and taking a bogey at the par-3 15th, Cink eagled the par-5 first, reaching the green in two and sinking a 20-foot putt.
He followed a 10-foot birdie putt at the second hole with a three-putt bogey at the third and, after a five-foot birdie putt at 14, missed a chance for the solo lead when a tee shot way right beyond a cart path at the ninth led to a closing bogey.
Cink made his 500th career PGA cut.
"To make 500 cuts, I think that's pretty respectable," Cink said. "I'm proud of that."
'A grinding round'
Streelman, 45, seeks his third PGA title but his first since the 2014 Travelers Championship. He led after 18 holes with a 64 but stumbled a 72 on Friday.
"Definitely a grinding round," said Streelman. "I'm very happy with it. I knew it was going to be very difficult."
Hughes, 33, seeks his third PGA crown and his first since the 2022 Sanderson Farms Championship.
Todd, 38, chases his fourth PGA victory and first since Mayakoba in 2019.
Phillips, 27, is playing in only his 12th PGA event and has never finished in a tour top 20.
The sixth-place pack on 137 included Americans Justin Thomas, Lucas Glover, Peter Malnati, Michael Kim, Scott Stallings and Keith Mitchell plus Ireland's Seamus Power and Australian Aaron Baddeley.