Crane's round was enough to see him come from behind and grab a one-stroke lead on 14 under par heading into the weekend at the Port Royal course in Southampton.
The 46-year-old American made nine birdies, two bogeys and an eagle to match the best round of his PGA career.
"Today was one of those special days, one of 100 where it just kind of all comes together," Crane said. "So really cool to shoot 62."
"That 29 on the back, I didn't see it coming. Super fun day."
As many as five players lie just one shot behind, including Australia's Aaron Baddeley and Americans Adam Schenk, Ben Griffin, Robby Shelton and Austin Smotherman.
Crane admitted he was just happy to be playing after getting a sponsor's exemption, but he's hoping for even more on the weekend.
"Couldn't be more encouraged," Crane said. "Played the best golf I've played in a long time and to be in this tournament is super encouraging. I don't get in a lot."
Crane is a five-time PGA Tour champion but the last of those victories came back at the 2014 St. Jude Classic and he missed the cut in seven of 10 starts last season.
Baddeley was playing alongside Crane and the duo seemed to feed off each other, as the Australian fired eight birdies against a single bogey.
"Feel like the confidence is back," he said. "Just a matter of just getting some starts. So it has been great."
India's Arjun Atwal, who shot a 63 Thursday in his first PGA Tour round for three months since his father's death, carded a 71 to lie six shots off the pace.