Matt Duchene had a goal and two assists for Colorado (12-2-0), which fell one win short of NHL history. The Avalanche were attempting to set a franchise record and match the 2007-08 Ottawa Senators for the best 14-game start in league history.
"When you have a taste of winning -- to use a bad analogy -- it's like a drug. You crave it more and more," Duchene said. "It feels terrible and we've felt this twice this year and it feels awful. It feels that much worse. When you're used to losing, it's just another game, but when you're used to winning it hurts that much more."
After finishing with the worst record in the Western Conference last season, the Avalanche are near the top this season.
"As much as I wish to be 81-1, it's a little tough," Colorado coach Patrick Roy said. "They're a good team; it's a nice way for us to learn."
It took a career game from Wilson, who has worked his way back from a shoulder injury in March that ended his 2013 season. He had four points March 8, the game before he was hurt.
"Obviously, it was great getting some numbers, getting the puck in the net, just to remember I can do it," Wilson said. "It was a while ago that I got injured, so it was good to get back at it."
The Predators appeared to take control when Gaustad and Wilson scored early in the second to give them a 4-2 lead. Paul Stastny got one back with a power-play goal with 6:27 left in the period, and Duchene tied it 4:23 into the third.
Wilson answered with his second goal of the night when he beat Semyon Varlamov at 7:34.
"I felt the pressure on my back and I was going to slip it five-hole but decided to move it really quick to my backhand," Wilson said.
Varlamov finished with 22 saves while allowing a season high in goals.
"It's always tough to give up five goals," he said. "It was not my greatest game this year."
The Avalanche pulled Varlamov for an extra skater with more than a minute left, and Gabriel Bourque scored into the empty net.
Nashville goalie Carter Hutton made 11 of his 27 saves in the third to preserve the win.
The teams, now in the same division, found a reason to ramp up the rivalry when Colorado forward Jamie McGinn left his skates to check Nashville rookie defenseman Seth Jones into the boards. Jones stayed on the ice for a moment before skating to the bench under his own power.
He went to the locker room but returned late in the period.
"My face kind of went into the boards, bit my teeth a little bit but my head was fine," Jones said. "I was [worried] but I kind of knew right away when it happened. I went directly to my teeth and I didn't have a headache."
McGinn was given a charging minor and the Predators capitalized with Smith's third goal to give Nashville a 2-1 lead.
"You could see Seth was putting the brakes on, he's got his back turned, he's exactly what we talk about being a vulnerable player," Nashville coach Barry Trotz said. "McGinn takes the two or three hard steps and then I thought he left his feet.
"I just thought he hunted him out and he was a vulnerable player, and that's what we're trying to take out of the game."
Stalberg opened the scoring with his first goal of the season at 13:12 of the first, and P.A. Parenteau tied it with his fifth 2:11 later.
Ryan O'Reilly scored early in the second for Colorado.
Ryan Ellis and David Legwand had two assists each for Nashville. ... McGinn returned to the lineup after missing three games with a knee injury. ... Nashville C Matt Hendricks missed his second game with an upper-body injury while C Mike Fisher missed his first game with a lower-body injury. Both players are day to day. ... Avalanche LW Alex Tanguay will miss two weeks with a knee injury sustained in Saturday's win over Montreal.