Rinne made 17 saves for his fifth shutout of the season, and Colin Wilson, Jason Arnott, and Patric Hornqvist each had a goal and an assist in the Predators' 5-0 victory over the Wild on Thursday night.
Nashville won its fourth straight, ending Minnesota's winning streak at three.
J.P. Dumont and Marcel Goc also scored for Nashville.
Entering Thursday, Minnesota was 10th in the Western Conference standings, six points behind eighth-place Detroit, but any hopes of gaining ground on the Red Wings were dashed early as the Predators struck for three goals in the opening period.
Wilson opened the scoring at 7:07. Inside the Nashville blue line, Wilson blocked a shot by Minnesota defenseman Nick Schultz. Wilson then carried the puck into the Wild zone along the right side before cutting to the middle and slipping a wrist shot by goalie Josh Harding on the far side.
"We got a couple of key goals early to get us going on the right track," Wilson said.
Just under 2 minutes later, Dumont beat Harding with a shot from the high slot.
With 39 seconds remaining in the first, Arnott's shot from the right boards beat an out of position Harding.
"We played well with the lead, and we played with confidence at the end of the game," Arnott said. "Everybody contributed tonight and we came out with a big two points."
Goc scored at 2:19 of the second, and Hornqvist connected on a power play at 7:35 of the third.
"We stayed really disciplined in a lot of areas," Nashville coach Barry Trotz said. "I thought we were really good in the faceoff circle tonight. They are a team that can really create off of the draws."
Nashville won 42 of the 67 faceoffs.
"I thought it was the start that we wanted; we generated a couple of good opportunities, but we weren't able to score," Minnesota coach Todd Richards said. "We lost a lot of battles and spent a lot of time in our own zone."
Rinne was tested early, seeing nine Minnesota shots in the first period, but saw just four in the second and four in the third to record his 12th career shutout.
"In the first period both teams had chances, but we got those goals, and I think it kind of took the wind out of them," Rinne said. "We didn't let up after that and kept pushing the game."
Wade Dubielewicz replaced Harding in the Minnesota goal to start the third period.
"We weren't that good today," Harding said. "The great thing about hockey is that we can forget about this one and get ready for tomorrow. I think we all know we need to be better."
NOTES: Nashville improved its record against Northwest Division opponents to 12-7-1 ... Wild D Greg Zanon played in his 300th career NHL game. Zanon's first 230 games were played with Nashville. ... Nashville C Dustin Boyd had an assist for his first point as with Nashville. ... Predators RW Martin Erat had two assists to extend his points streak to three games.