The struggling Predators looked like they were headed for their third consecutive loss when they entered the final two minutes of regulation trailing 3-1. But Patrik Hornqvist scored with 1:36 remaining to make it a one-goal game before Kostitsyn got the Predators one point.
Wilson earned the other one when he finished off a slick pass by Martin Erat on a 2-on-1 break.
"Marty likes to pass on those 2-on-1s," Wilson said. "I just want to get open. I opened up for him real quick, and he put it right in my wheelhouse. I let a quick shot go."
"Today we found a way to get it done," Nashville coach Barry Trotz said. "That's more like the Predators I know."
Hornqvist gave Nashville a chance when he whacked in the rebound of a Shea Weber blast. Nashville then received a power play with 1:06 when the Jackets' Samuel Pahlsson was called for cross checking. The Predators pulled goalie Pekka Rinne for a 6-on-4 advantage, and after Nashville won a faceoff in the offensive zone, Erat tossed the puck toward Kostitsyn in the high slot for a tip that beat Curtis Sanford.
"The last two minutes, we were really pushing hard," Hornqvist said.
The Jackets looked like they were on their way to victory when Dorsett split two defenders before snapping a shot past Rinne at 1:24 of the third period.
"We allowed Weber to get the shot away on the first one," Columbus coach Scott Arniel said. "(Then) a (bad) makeup call by the referee that was horrendous on Sammy Pahlsson, who's never been in a fight in his life. And he calls that call there. In a 6-on-4 you know they're going to be teeing off and making their plays."
The Jackets did little in the overtime before Wilson's winner.
"We had chances to clear pucks 200 feet, and we didn't do it," Arniel said. "Once they tied it up, we were pretty rattled after that."
Columbus took a 2-0 lead at 10:49 of the second period when Vermette picked up the rebound of Jared Boll's shot, deked Rinne and slipped a backhander under his blocker.
Nashville got on the board at 13:10 when Francis Bouillon's slap shot from the point was stopped by Sanford, but Kostitsyn was in the slot to chop the puck to Fisher, who was crashing the net and jammed it in for his sixth of the season.
The Blue Jackets took a 1-0 lead 12:42 into the game, though they needed a little extra time to find out.
Vinny Prospal set up behind the cage and tried a wraparound that was deflected to the stick of Carter, who was straddling the left goal line 15 feet from the net. Carter's rocket went behind Rinne and off the back crossbar inside the net. But since the puck rocketed off the metal bar and out the other side instantly, play continued.
It wasn't until the next play stoppage, about 30 seconds later, that NHL officials in Toronto looked at a video review and told referee Gord Dwyer that the shot went into the net -- surprising even Carter.
Material from team media and wire services was used in this report
1 - 0 CBJ
2 - 0 CBJ
2 - 1 CBJ
3 - 1 CBJ
3 - 2 CBJ
3 - 3 Tie
4 - 3 NSH