Neal scored late in the third period to give the Predators a 2-1 win over the Vancouver Canucks on Tuesday.
"Stanley Cup important I think you can say, playoffs important," Neal said of their current run. "We’re fighting to play for a Stanley Cup here. And right now with how tight the West is, you have to do anything you can to grab points to get into the playoffs.
"That’s where our team is at."
It was Nashville's third win of a four-game Western road swing. The trip has included 4-1 wins in both Winnipeg and Edmonton and will finish Wednesday in Calgary. The Preds are sixth in the Central and one point behind Minnesota and Colorado for a wild-card spot.
Neal made the Canucks pay for a bad line change with 4:44 left in the game. He took a pass from defenceman Barrett Jackman and fired the puck from the faceoff dot, beating goalie Ryan Miller glove side.
"We have talked about (line changes)," said Canucks head coach Willie Desjardins. "It's something that we need to be better at. Those are tough points to lose, on something you could have avoided."
Brandon Sutter scored for the Canucks (20-19-11), who played their last game before the all-star break. Vancouver just returned from a 10-day, six-game road trip that resulted in a 3-2-1 record.
Miller made 17 saves in his first home start since Dec. 9 for Vancouver, which is fifth in the Pacific tied with Anaheim at 51 points.
Despite the loss, it was a triumphant comeback for Sutter. The forward hadn't played since sustaining a sports hernia on Nov. 10.
"It felt good (but) it takes a little time," said Sutter. "The body felt good. It's a nice relief to get that over with."
Sutter, thrusted into the centre position on the top line due to Henrik Sedin's injury, found immediate chemistry with Daniel Sedin. He took a beautiful return pass from Sedin and one-timed it past Rinne to tie the game at 11:39 of the first period.
Sutter had a glorious chance on a shorthanded breakaway minutes later, but missed the open net with Rinne out of position.
"I don't know what happened," Sutter said. "I missed the net by two feet. It's unfortunate but that's part of the game."
Nashville jumped out to a quick 1-0 lead less than two minutes into the game when Mike Fisher set up Smith, who lifted the puck over Miller's shoulder after easily getting around Canucks defenceman Ben Hutton.
The Predators shot sparingly in the first and second. Even with two power plays, including a tripping call on Matt Bartkowski midway in the second, Nashville only had 11 shots going into the third compared to Vancouver's 24.
Nashville came out with increased intensity in the third and began firing more shots at Miller.
"It was a good third period by our guys," said Nashville head coach Pete Laviolette. "We were kind of sleeping for a little bit, but third period we were really good.
"I think the guys know exactly where we are at when the game is on the line in the third period. Our third period was excellent the first two games of this trip and it was excellent tonight."
Notes: Vancouver forward Brandon Prust was a healthy scratch for a third straight game. ... Henrik Sedin missed his fourth straight game with a upper-body injury.