Nashville goaltender Pekka Rinne made 36 saves, including all 14 shots he faced in the third period, for a 3-1 win at Xcel Energy Center.
Rinne leads the NHL with 28 wins.
"He was really good," Predators coach Peter Laviolette said. "There were a couple of saves in the first, and two or three more in the third. I think our guys did a decent job in front of him, but there were a couple opportunities where we needed him to step up and make some big saves."
"In the first two periods, we got caught making plays through the middle and that fed into their game." said Predators forward Colin Wilson, who had a goal and an assist. "We got away from that [in the third period], started getting pucks in behind them and making plays. That's how we win."
The Wild ended a three-game homestand 0-2-1 and are 1-3-4 in their past eight home games dating to Dec. 17. Minnesota (18-17-5) has lost four in row, 10 of 12, and has fallen into last place in the Central Division.
"It's been something different every game. We're spinning our tires right now," Wild coach Mike Yeo said. "We have to find a way to win hockey games. As lame as that might sound, that's what it is. It's a mindset and an attitude right now."
Nashville (28-9-4) took the lead 4:01 into the game after a defensive miscue left Mike Fisher alone in front. Wilson won a puck battle along the end wall and centered it to Fisher, who roofed a backhand past Backstrom for his seventh goal of the season.
"I was just forechecking and I noticed the [defenseman] was trying to reverse it," Wilson said. "So I just got my stick in there and it popped up. I was fortunate to grab it and I saw [Fisher] coming in. He made a great play bringing it from his skate to his stick and burying that goal."
Minnesota controlled play for much of the first period and tied the game at 14:14. After Wild forward Nino Niederreiter beat out an icing, defenseman Christian Folin pinched into the corner to retrieve a loose puck. He threw it toward the net, where it landed on the tape of Charlie Coyle on top of the blue paint. He had an open net for his fourth goal of the season at 14:14.
Each team had nine shots in a scoreless second period, but the Predators killed three penalties when the Wild had a chance to take the lead. Minnesota went 0-for-5 on the power play.
"We had a chance to grab a hold of the game in the second period and instead we let it slip away," Yeo said. "I always think that shooting the puck brings a lot of momentum, especially at home. We didn't have that feel tonight."
Nashville scored with 11:13 remaining in the third period when Wilson was gifted a turnover by Wild defenseman Justin Falk. The puck came right to Wilson, who was alone in front and flipped a backhand through Backstrom's five-hole.
"It was just a bad bounce," Falk said. "I'm going to try that play every single time. It was just a bad break."
Wilson said, "I was surprised. I don't know if it was a mishandle or what, but [it] came out to me in the slot ... I'll take those."