Columbus has allowed four shorthanded goals in 15 games this season.
"We played good defensively," Korpisalo said. "Of course, mistakes happen every game. You can't do anything with that."
The Blue Jackets came close to tying it in the third period, but Kukan's shot from the right point hit the left post at 5:32, and after Fleury made the save on Seth Jones' shot from the slot at 10:24, Golden Knights defenseman Jon Merrill stretched to clear the puck from in front of the goal line.
"We were pretty resilient just trying to clear the front of the net tonight," Smith said. "[Fleury] made a lot of big saves, but it seemed they had a lot of ways to pressure and they were creating chances.
"It was nice to see it go our way after the last couple went the opposite way. It's frustrating, so it's nice to get a win like that, especially on the road to start a long road trip."