The former world number one began his final round 10 shots off the pace, but carded a five-under par 67 to close the gap on overnight leader Kim Hyung-tae, who visibly buckled under the pressure.
He went round in six-over par and ended up level with McIlroy on three under for the tournament, allowing Kang to snatch victory with a birdie on the last at the Woo Jeong Hills Country Club.
"I could have shot anything, absolutely anything," McIlroy told reporters. "I only missed two greens and had so many chances, but it was like the story of yesterday - I just didn't hole enough putts.
"I created so many more chances today that it could have been 61, 62. It just wasn't to be."