Pouliot returned to the lineup after he was a healthy scratch on Tuesday.
"I was kind of off the past few games and that's why I sat a couple games," Pouliot said. "Tonight I was trying to do as much as I could in front of the net. [Jack Eichel] and [Okposo] are so good with the puck in the corners and getting off checks and stuff for me just to go in front and get the chances."
Okposo made it 2-0 at 7:18 of the third period when a puck dumped into the Blue Jackets' zone by Evander Kane took a funny hop off the Zamboni door in the corner right to Okposo, who shot it past Bobrovsky after the goalie left the net to play the puck.
"That's a little gift from the hockey gods tonight for me and for the team," Okposo said. "It was a nice bounce to get. I felt like just trying to work, and when you work you seem to get those bounces. And there's times when you're not going to get them so you've got to take them when they're there and try to keep working to create your own luck."
Rookie defenseman Brendan Guhle assisted on Okposo's goal for his first NHL point.
Panarin made it 2-1 at 13:45 with a power-play goal when he skated through the neutral zone and toward the Sabres' net, deked, and took a backhand shot that beat Ullmark over his left shoulder for his 12th goal.
"I've been impressed with [Panarin] from Day One as far as what he can do," Blue Jackets coach John Tortorella said. "That goal he scores, he's on the ice for two minutes prior. Yeah, he's an impressive player."