Zach Parise made it 4-1 at 9:10 with a backdoor redirect at the left post off a pass from Noah Dobson.
Gavrikov cut it to 4-2 at 13:32. His initial shot was blocked in the low slot, but he followed the play and scored on a backhand.
"He's usually at his best at the other end, but obviously a [heck] of a goal scorer as well," Laine said. "It was kind of nice the D is starting to activate a little bit. He made great reads on both goals."
Oliver Bjorkstrand scored at 4:30 of the third period for the 4-3 final.
Columbus outshot New York 16-3 in the third.
"The first two periods, we were fine," Trotz said. "We played well. I thought in the third period, we just sat back. We just didn't play."
NOTES: The Blue Jackets were without coach Brad Larsen and assistant Steve McCarthy, who entered NHL COVID-19 protocol before the game. Assistant Pascal Vincent ran their bench. … Nelson's goal was the 200th of his NHL career. He has scored 13 goals in March, the most in a single month by an Islanders player since Zigmund Palffy scored 13 in March of 1996. … Cory Schneider was recalled by New York from Bridgeport of the American Hockey League and served as the backup goalie. Ilya Sorokin did not travel after he sustained an upper-body injury in a 4-1 loss to the Tampa Bay Lightning on Sunday. … Islanders forward Matt Martin played his 800th NHL game. … Columbus defenseman Andrew Peeke had an assist in his 100th NHL game. … Bjorkstrand set an NHL career high in goals (24). He scored 23 in 2018-19. … Blue Jackets forward Jakub Voracek has a six-game point streak (two goals four assists).