"We've got to get as many shots on net as possible," Blue Jackets forward Brandon Dubinsky said. "We have to do a better job of getting inside and getting some of those rebounds and tips. You saw that's where they score their goals."
Panarin cut the lead to 2-1 at 9:53, redirecting a pass from Cam Atkinson in front of the net, but Sheahan scored his second to make 3-1 at 11:29.
The Penguins scored on three of their first four shots.
"They have a lot of offensive weapons," Atkinson said. "It's tough chasing the game, especially against a team that's so offensive-minded."
Zach Aston-Reese made it 4-1 at 9:29 of the second on the rebound off a Matt Hunwick shot for his fourth goal in his past four games.
"When we got a three-goal lead like that early in game, it's a dangerous lead," Penguins coach Mike Sullivan said. "As much as we're pushing our guys to pay attention to detail and stay on top of it, you're fighting human nature to a certain extent.
"And give Columbus credit. They were fighting all night long. They're a good team. They played hard, they put us under pressure."
Wennberg scored to make it 4-2 at 2:21 of the third period before Guentzel extended the lead to 5-2 at 14:09 with a slap shot from the left circle that beat Bobrovsky short side.