Play was not stopped when the puck hit the netting, and the play was not reviewable because Panarin was not the first player to touch the puck afterward.
"It's easy to lose your composure when something like that happens, something out of [your] control," McAvoy said. "Credit to us to staying with it, realizing there's still a lot of hockey to be played."
Kuraly made it 3-1 from the low slot at 8:40 of the third period after a pass off the end boards caromed to Bobrovsky, who tried to clear the puck but had it deflect off Blue Jackets defenseman David Savard.
Bergeron scored on the power play with 2:30 remaining, poking in a rebound of a Pastrnak shot to make it 4-1.
Boston was 2-for-6 on the power play and 4-for-4 on the penalty kill.
"We've kind of prided ourselves on being disciplined and that's the most disappointing part," Columbus coach John Tortorella said. "Their top guys score some goals on the power play. We gave them a chance to get going now by just sitting in the box too much."