The Blue Jackets outshot the Oilers 21-7 in the first period.
"I felt good. I think we still played pretty well, we kept them on the outside," Koskinen said. "They got a lot of shots, but most of them were from the outside. I think it was big that we kept them down in the first, and after that we got a little bit better, and it was a big win for us."
Emil Bemstrom had a chance to tie the game at 10:49 of the third period after he got a loose puck during a scramble in front, but he was unable to lift it over Koskinen and into the top of the net, hitting Edmonton forward Leon Draisaitl to the left of the crease instead.
"I don't think we could have played any better," Blue Jackets coach John Tortorella said. "We just played good as a team. We played good as a team away from the puck. Their goalie is the difference. That's the difference in the game, their goaltending."
Caleb Jones scored on a shot through traffic at 15:29 to put the Oilers ahead 2-0, and Connor McDavid scored at 16:25 off a pass from Zack Kassian to make it 3-0.
"That's the way we have to play. I thought we played a good game," Columbus defenseman Zach Werenski said. "It's a tough outcome, but that's part of hockey, and right now we have to find a way to get two points no matter who we play. I think we can take away a lot of positives going into tomorrow night (at the Vancouver Canucks) and we just have to tell ourselves this is how we have to play. If we play like that, I think we're going to win a lot more games than we're going to lose. It's just unfortunate tonight we came out on the wrong side of things."
After Nyquist's goal made it 3-1, Riley Sheahan scored into an empty net with 30 seconds left for the 4-1 final.