Wilson was able to collect a rebound of a shot by Craig Smith and put it in a wide-open net.
"We were just hard on the puck and I got it over to [Calle Jarnkrok] and Jarnkrok got it over to [Smith]," Wilson said. "He had a good shot. I just had to put it in the net."
Wilson's goal was his sixth point in the past six games. He's finding some chemistry with Jarnkrok and Smith.
"He's been excellent all year, and he's one of those guys that maybe the points weren't coming at the beginning of the year maybe as frequently as he would like," Predators coach Peter Laviolette said of Wilson. "That's something that we don't really talk about internally. We don't say you've got to get going scoring some points. We talk about our team and what we need to do in order to be successful, and he's been terrific."
Nashville finished 4-0-0 on its homestand, and goaltender Pekka Rinne has won six in a row. Rinne's 16 wins are the most in the NHL.
"He's a goalie that bails you out when you make mistakes," Predators forward Mike Ribeiro said. "That's why they're there I think, that's their job. When the team in front of you makes a mistake, they're there to cover up. He's been huge for us, and it makes everyone more confident in front of him. Your best player has to be your goalie, and I think he's been our best player every night."
Nashville (16-5-2) is winning close games it didn't win last season, and that's been a big reason for its success.
"It doesn't matter if we're down one or up one or if it's tied," Predators defenseman Roman Josi said. "We know we have a chance to win the game. We never get ourselves out of the game and just keep going at it. I thought we played a really good game and deserved that win."
Columbus (6-15-2) is winless in its past six games. Coach Todd Richards said the Blue Jackets have to start finding ways to get a point in games like this one.
"We've got to find ways to win hockey games," Richards said. "Our goaltender was very good (Curtis McElhinney, 40 saves), kept us in it. We found a way to tie it up and had a chance. I'm talking about just getting it to OT and getting a point. Obviously we failed at that."
Nashville outshot Columbus 20-7 in the first period with several point-blank chances McElhinney was able to stop.
Ribeiro put the Predators up 1-0 at 12:47 of the second period on a wraparound. Josi took a shot that went wide to Ribeiro behind the net, and he was able to beat McElhinney to the post.
Nashville held a 34-15 shot advantage through two periods, and finished with a 42-22 edge.
Columbus forward Ryan Johansen scored his ninth goal of the season to tie the game 1-1 at 3:48 of the third period. A 5-on-3 power play had expired, and Johansen was set up next to Rinne, where he was able to convert a pass from Nick Foligno.
"We did a lot of good things tonight that we will be able to look at and show the guys," Johansen said. "There are some things we still need to get better at, and we have to find ways to capitalize on opportunities right now."
The Predators are 10-1-1 at home. Nashville didn't reach 10 wins at home in 2013-14 until Dec. 30.
"I think we've been playing some really good hockey, and we just work hard every game," Josi said. "Our fans have been great. They were loud again tonight. They're loud if you have a big shift. Even if you don't score, they cheer for us. That definitely gives us that extra jump."
Nashville went 0-for-4 on the power play, which makes them 1-for-41 at home.
Columbus forward Artem Anisimov sustained an upper-body injury in the second period and did not return.
Predators forward Matt Cullen returned after missing a 1-0 overtime win against the Edmonton Oilers on Thursday with an upper-body injury. Cullen took the place of Derek Roy, who was out with an upper-body injury.