Martin Erat scored with 8.4 seconds left in 5, at Bridgestone Arena.
The comeback nullified a hat trick from Blue Jackets forward Jeff Carter, who recorded all three scores in a first period which saw the visitors emerge with a 4-1 advantage.
"I've been a part of different types of comebacks over the years," said Nashville head coach Barry Trotz. "I didn't think we played bad and yet we were down 4-1. I said after the first period that (Columbus' lead) came too easy. All you have to do is chip away."
David Legwand scored the tying goal with 3:46 remaining for the Predators, who have won six of their last seven.
Ryan Johansen notched the other two goals for the Blue Jackets, losers of four straight and six of seven.
Curtis Sanford was shelled for all six goals on 38 shots.
After several close calls throughout the third period, Nashville finally drew even inside the final four minutes as Colin Wilson fished out the puck behind Sanford, circled the net and fed Legwand for a slam-dunk at the right post.
The game seemed to be destined for overtime, but Ryan Suter was allowed to send a pass right up the middle for Erat, who stickhandled past two defenders and slid the puck between Sanford's pads for the deciding tally.
"I was just flying through the middle of the ice and not really paying attention to where their defense was," said Erat. "I saw that I was on a breakaway and just tried to make a quick move to my backhand."
Fisher's rebound power-play goal at 12:29 put the Preds on top, but Carter responded 27 seconds later with a wicked one-timer from the right circle off a feed from Vinny Prospal.
After Preds enforcer Brian McGrattan was given a major for boarding Jared Boll along with a game misconduct, Carter struck at 14:35, then Columbus went up 3-1 at 15:30 on a Johanson power-play marker from the right circle.
The trifecta was completed for Carter only 44 seconds later, as he fought in front and managed to backhand a Rick Nash rebound past a diving Rinne at the left post.
Hornqvist got one back for Nashville less than 5 1/2 minutes into the second when he finished off a slick passing play between Legwand and Shea Weber, but Johanson notched his second power-play goal of the game with less than eight minutes elapsed.
Spaling pulled the home squad within 5-3 at 8:53 on a redirection of a Wilson pass during a delayed penalty, and Josi made it a one-goal margin with 6:19 remaining on a rising slapshot from the right wing.
"We play a great first two periods for so many games, and in the third periods, we just collapse," Johansen said. "We practice all week working on our third periods and things we should do a little smarter, and to get a loss again in the third period like that is tough."
Nashville has won 18 of the its 19 home games against Columbus, and successfully avenged a 4-3 Blue Jackets' overtime victory on November 19...Thursday's tilt marked Carter's first three-goal game with Columbus and his first since November 11, 2010 at Carolina with the Philadelphia Flyers...Carter's hat trick was the first for Columbus since Matt Calvert turned the trick on February 25 against Phoenix...Weber ended up with three assists, while Suter and Wilson were credited with two helpers each...Derick Brassard, R.J. Umberger and Nash totaled two assists each for the Jackets...Johansen snapped a 16-game goal drought.