The Blue Jackets are 1-8-3 in their past 12 games and 3-14-4 in their past 21.
The Predators have won four of five and are 5-1-1 in their past seven games.
"This time of year, like the playoffs, you may not play your best game," Predators coach John Hynes said. "You may be in a situation where like tonight we had the lead and we gave the lead back into a tie game but I think the most important thing obviously is you have to find ways to win,"
The teams play again here Wednesday.
"This is the best time of the year. This is great," Forsberg said. "You want to play these types of games. … They mean so much."
Bemstrom scored at 1:54 of the third to make it 3-1. His first shot was saved but he batted in the rebound at the left post. The goal was upheld after being reviewed to see whether it crossed the goal line and if it had been hit with a high stick.
He made it 3-2 at 7:26 from the left circle and tied it 3-3 from the left dot with a power-play goal at 15:07. It was his first NHL hat trick.
"Hopefully [I'll] build some confidence over the next three games and be confident next year," Bemstrom said.
Bemstrom missed 21 games since March 18 with a lower-body injury before returning Saturday in a 2-1 overtime loss at the Carolina Hurricanes.
"He can shoot the puck, and it's not a secret it's been a tough year for a lot of guys with everything going on," Del Zotto said. "For him to perform the way he did tonight, I'm super proud of him."
Forsberg gave Nashville a 1-0 lead at 9:01 of the second period, scoring from the slot on a rebound of a shot by Ryan Ellis.