Kim started the day one shot off joint third-round leaders Brooks Koepka and Min-Woo Lee, with Ko and Smylie one further back.
Ko eagled the 17th and then headed into the clubhouse tied for the lead with Smiley after both shot 65s.
Neither the former world No 1 Koepka nor Lee could respond to that closing spurt.
The American went out in four under but came home in one over par, for a 68. Australian Lee had three bogeys on the back nine for a 69.
Kim picked up two strokes on the last three and held his nerve on his way to a 65 and a 16-under four-round total. It was enough for his first European title and his first anywhere in seven years.
“It feels amazing. I haven’t won a tournament since 2018 at the John Deere Classic,” he said.
“I’ve had a really good year on the PGA Tour this year. This feels like the perfect cherry on top and I hope to continue this throughout my career.”