The Blue Jackets (9-6-1) are 0-2-1 in the past three games.
Columbus rookie forward Pierre-Luc Dubois tied the game 1-1 at 4:37 of third period with his second goal and first since opening night against the New York Islanders on Oct. 6. He stripped the puck from P.K. Subban at center ice and scored on a breakaway.
"I read it," Dubois said. "It all happened so fast so I decided to go on him. Any other night it might have been a mistake. I'm just happy it went in."
Jarnkrok scored his second of the season at 14:25 with a rebound from the slot after a shot by Miikka Salomaki to make it 2-1. The play withstood a challenge by the Blue Jackets of goaltender interference on Joonas Korpisalo, who made 26 saves.
Irwin gave Nashville a 1-0 lead at 12:36 of the second after Arvidsson did the work along the right wall. He shirked a check and skated through the bottom of the circle, placing a cross-ice pass to an open Irwin for a shot under the crossbar.
Irwin has two goals in the past three games.
Columbus, which allowed three goals on five Rangers power plays, killed all four Nashville tries.
"Penalty kill played really well tonight," Blue Jackets defenseman Seth Jones said. "We didn't let them get set up that much."
Nashville was also 4-for-4 on the kill, including a tripping penalty to Filip Forsberg with 5:10 left in the third period.
"There's a factor of desperation," Rinne said. "That's what you need when you play in other team's buildings."
Center Kyle Turris, acquired Sunday in a trade with the Colorado Avalanche via three-team deal with the Ottawa Senators, has not joined the Predators while waiting for the immigration process to be completed.