But he birdied eight, nine and 10, and settled down on the back nine as he regained the form that saw him shoot a second round 61.
Momentum swung decidedly in the 31-year-old's favour on the par-four 15th when he sank a 23-foot birdie putt for the outright lead. He held the advantage en route to a four-under 67, for a 23-under 261 total.
Matt Every, who had been neck-and-neck with Kang all day, had a costly bogey on 15 and never threatened after that, finishing tied for second with Scott Piercy at 21-under 263.
An exhausted Kang said he decided to just relax and have fun despite a lack of sleep, with Saturday's play suspended for darkness and the third round completed earlier on Sunday.
"Yesterday we finished too late and I didn't get enough time to sleep. I only slept about three hours," he said.
"When my turn came up I tried to really focus on it and it worked out great. I am so happy right now."
Kang embraced his wife and eight-month baby on the green after sinking the final putt, a Mother's Day his family, who live in the Dallas area, will not soon forget.
The win is a breakthrough for Kang, marking his first victory in 159 PGA Tour starts.
The success is also indicative of the rise of Koreans on the Tour. In 2003, K.J. Choi was the only South Korean-born player and today there are 15.
The result was bitter for American Every, who needed to win to qualify for next week's PGA Championship, but encouraging for countryman Piercy, who posted four bogey-free rounds.
It was also a good week for world number three Brooks Koepka, who had an eagle and four birdies in his bogey-free final round to finish fourth on 20-under.
Koepka will look to keep the momentum when he defends his PGA Championship title at Bethpage Black in Farmingdale, New York next week.
(Reporting by Rory Carroll; editing by Tony Lawrence / Ian Ransom)
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