Americans Matt Every (65) and Tyler Duncan (66) were equal second on 12-under, with big gun Brooks Koepka (66) a stroke further back.
But former Dallas Cowboys quarterback Tony Romo will be benched on the weekend, after carding 74 to miss the cut by 10 strokes.
"I live in Dallas and I've never seen the weather like this in May," said 31-year-old Kang.
"I checked the weather yesterday and I knew it was going to be really cold and windy so I tried to prepare for how far the ball was going to go this morning and it worked out great.
"It was so cold I couldn't really move my body but I missed it in the right spots where I needed to miss it."
World number 138 Kang has not had a decent result since a tie for sixth at the Arnold Palmer Invitational in March and is seeking his first PGA Tour win.
Koepka sounded up for the chase.
"I don't need to catch him tomorrow ... but I feel like I'm playing really well and I like my chances," he said ahead of his PGA Championship defence next week.
Local Jordan Spieth also showed form before his next attempt for a career grand slam of majors.
"Very pleased," a beanie-wearing Spieth said after his 67 left him nine shots behind Kang.
"I improved on yesterday which already was a solid day. I feel good on the greens. One or two tee balls cost me a shot or two but all in all we had some very difficult conditions."
Spieth marvelled at Kang's score.
"What Sung is doing now is absurd given what we faced," he said.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Ian Ransom)
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