"I'm so happy right now", Kang said after notching his first tour win in his 159th start.
Tyler Duncan, also in the final threesome, was third at 15 under a day after his wayward tee shot on his only bogey in the second round hit his wife on the head - she was OK.
He finished his third round with a 70 and is T5 entering Sunday's final round at Trinity Forest.
Kang, who said he unexpectedly felt calm throughout the round, had just three-putted for his first bogey in 38 holes. "I just needed to keep making birdies". His best Nelson finish is still a tie for 16th in 2010 when he played in the tournament for the first time as a 16-year-old amateur on a sponsor exemption.
World number three Brooks Koepka finished strong, carding a six-under par 65 to finish alone in fourth on 20-under 264 heading into his PGA Championship title defence at Bethpage Black next week.
Every had edged ahead by one through nine holes when darkness halted play on Saturday.
His chance looked to have gone when he surrendered a one-shot lead with bogeys on the 15th and 16th, but the 22-year-old Swede recovered to finish a shot ahead of defending champion Eddie Pepperell (66), Matt Wallace (71) and Robert MacIntyre (68).
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But Kang fired three birdies and bogey over the final nine holes of the third round to regain a three-shot lead. His ball settled in some nasty rough well below the hole, and his shot from there got to the top of the hill before rolling back into a bunker.
Because he knew it would be hard to concentrate, Kang said he told his caddie "I just wanted to be chill and having some fun and then when my turn came just try to really focus in - and it worked out great". "I was telling my caddie I'm really exhausted".
Kang had to play 27 holes and said he made a decision to just relax and have fun despite a lack of sleep.
This time, in a different part of Texas at Trinity Forest G.C. outside of Dallas, Kang also had a three-shot lead at the start of the round and this time finished off the task for the win.
Matt Every hits off the 10th fairway in the final round of the Byron Nelson golf tournament on Sunday, May 12, 2019, in Dallas.