Juuse Saros made 29 saves, and Ryan Johansen scored for the Predators (43-28-6), who lead the St. Louis Blues by two points for second place in the Central Division and trail the Winnipeg Jets by two points for first. It was their first win in three games.
"You work all year to work your way and get into the Stanley Cup playoffs, so tonight was the night we marked it," Nashville coach Peter Laviolette said. "Fifty percent of the teams, almost, don't make it. And it's not an easy thing. Everybody goes into the year with good intentions and everybody has a plan in mind and I'm sure they're all including the playoffs, so it's not an easy thing and should never be taken for granted, but our guys worked hard to get to this point. We have to continue to work on our game."
WATCH: [Predators vs. Wild highlights]
Minnesota (35-33-9), which has lost two straight and four of its past five games, remains two points behind the Colorado Avalanche for the second wild card into the playoffs from the Western Conference. Devan Dubnyk made 18 saves.
"Our backs are against the wall, but whether Colorado or [the] Arizona [Coyotes], whether they win or lose, we need to win," Wild forward Jason Zucker said. "For us, we obviously are going to need help, but we need to win. That's the only thing we can worry about."
Johansen made it 1-0 with a shorthanded goal at 4:32 of the first period, taking a pass from Viktor Arvidsson and scoring from the high slot. It was his first goal since Feb. 9 (20 games).
"It's a good feeling. You've really got to look at how hard it is to make the playoffs in an 82-game season," Johansen said. "It's a great accomplishment and it's something to be very proud of. At the same time, we have a goal in mind. There's a lot of work ahead of us still. We're going to keep our foot down."