The 25-year-old South Korean didn't flinch when Cantlay shot a 61 and surged out of 13th place to the front while breaking the Stadium Course record by two strokes.
Playing six groups behind Cantlay, Kim comfortably birdied the par-5 16th to pull even.
A year ago, Kim shot a 15-over 87 in the opening round on the easier neighboring Nicklaus Course before withdrawing.
Tony Finau had a 68 and finished fourth after starting the final round with a share of the lead in his quest to land his long-awaited second PGA Tour win.
The 28-year-old Cantlay made 11 birdies in the final round, including six in eight holes on the front nine.