Niederreiter scored an empty-net goal with 1:39 remaining in the third period. It was his 21st goal.
"It was my goal to get as many goals as possible," Niederreiter said. "I'm very happy that I had a chance to reach the 20-goal mark. I'm very proud of that, but I'm trying not to stop now."
Minnesota (32-22-7) has won four of its past five games and has jumped ahead of the Calgary Flames for the last wild-card spot in the Western Conference for the Stanley Cup Playoffs.
The Predators (41-14-7) had not lost at home since Feb. 5, when the Anaheim Ducks defeated them 5-2. They are 26-4-1 at Bridgestone Arena this season.
"I think to go into a building like this, I think that's maybe their fourth regulation loss, and they played a good game too," Wild coach Mike Yeo said. "It was an up-and-down game, but I do feel that we deserved the win tonight. We did a lot of good things. I thought the play of our defensemen was outstanding all night.
Forward Erik Haula gave Minnesota a 1-0 lead with 2:25 left in first period on a one-timer from the point that beat Rinne on the stick side. Justin Fontaine and Kyle Brodziak had assists on Haula's sixth goal.
"I feel like we were clicking early and could build some confidence getting a couple shots on net," Haula said. "It felt like we were just getting to pucks and just creating momentum from there."
"They came out hot and they played very, very strong," Niederreiter said. "We just had to make sure we played very solid and get the pucks out when we needed to, and I feel like that's exactly the way we played."
Brodziak gave Minnesota a 2-1 lead at 7:12 of the second period on a one-timer off of a faceoff win from Haula. Brodziak beat Rinne from the left faceoff circle before the Nashville goalie was able to react.
"They came out aggressively, had a good push early in the game," Brodziak said. "I think from the second period on, we really didn't feel like we played in the [defensive] zone too much, and when we were in there, we weren't giving them the high-quality chances like we talk about. And any chance we gave up, [Dubnyk], like he has been for the last who knows how long, has been great for us."
Predators forward Craig Smith tied the game 2-2 at 8:31 of the second period on a breakaway goal. He took a pass from Fisher and made a backhand-to-forehand move to beat Dubnyk for his 20th goal of the season, sixth in the past seven games.
"He was really strong tonight," Predators coach Peter Laviolette said of Smith. "His skating was sharp, and he seemed like he had lots of energy, lots of pop out there. He seems to be finding his way offensively with regard to scoring goals right now. He's a hot player for us."
"I really liked his game," Yeo said of Bergenheim. "A couple chances early in the first, I liked his wall play. Overall, I thought that it was a good, strong first performance."
"It was a starting point for him to get back out there," Laviolette said. "I think he played 12 minutes or so. It's hard when, in a game like this when it is a competitive team fighting for a playoff spot, there is not a lot of practice time to prepare for that. Just based on the season and the schedule, you get out there and do skating and shooting drills, but it doesn't really prepare you for the games. I think it's good to get him in there and progress from there."