Filip Forsberg and Eeli Tolvanen scored power-play goals in the third period as Nashville improved to 2-1 on its four-game trip. Roman Josi finished with two assists.
''It's a huge one,'' Rinne said. ''It doesn't matter who you play against, it's not easy to win. But I think it's important that we play the right way and we certainly did that tonight.''
Last-place Detroit lost for the fourth time in five games. Jonathan Bernier had 31 saves.
''He was unbelievable again tonight,'' Wings captain Dylan Larkin said. ''Our goaltending has been our backbone this season, without a question, and Bernie gave us a chance to win that game tonight. We need to go out and grab two points when we have an opportunity like this and we didn't do that.''
Nashville went ahead to stay on Forsberg's team-leading ninth goal 4:36 into the third. Forsberg's shot from the right circle fluttered over Bernier's glove.
The Predators added another power-play goal at 9:57. Forsberg passed to an open Tolvanen, who beat Bernier from the left circle.
''Of course when Fil gets the puck he can make the plays,'' Tolvanen said. ''We practiced that a couple days in practice. He's really good at finding the seams and it was pretty much an empty net when I got it.''
The Predators have scored 24 of their 41 goals in the third period this season.
It looked as if Nashville had jumped in front in the second when Forsberg put the puck into an open net. Detroit forward Adam Erne had run into Bernier, taking him out of position. But the Red Wings challenged for goaltender interference because Mikael Granlund's skate had hit Bernier's left pad, and the goal was nullified.
''It was nice after the goal got called back, I thought we stayed with it, came out in the third period, played really well,'' Predators coach John Hynes said. ''Special teams were a big difference in the game. I thought Peks held the fort well when they made a push later there in the third.''
The Red Wings came up empty on their only power play in the second. The league's worst power play hasn't converted an opportunity since Jan. 28 in Dallas, a 13-game drought.
''I thought our battle level was about 80%,'' Red Wings coach Jeff Blashill said. ''If we aren't close to 100%, we're not going to put ourselves in position to win hockey games.''
It was Rinne's 59th career shutout. He had three last season.
''He played unbelievable again,'' Forsberg said. ''I think he's been playing really well for us this season. There's been games where we haven't showed up in front of him and kind of left him out to dry. Today I thought we played solid defensively and whenever they got chances, especially a couple in the third there, he came up clutch and made some huge saves.''
Nashville forward Ryan Johansen was activated from injured reserve after missing seven games with an upper-body injury. Detroit forward Vladislav Namestnikov returned to the lineup after missing two games with a lower-body injury.
ON THE MOVE
The Predators recalled Tolvanen and defenseman Ben Harpur from the taxi squad and reassigned forward Sean Malone to the taxi squad. The Red Wings recalled forward Mathias Brome and defenseman Danny DeKeyser from the taxi squad and reassigned goaltender Kaden Fulcher to the taxi squad.
Forsberg's power-play goal extended his point streak against Detroit to six games. Josi has 11 assists in his last 11 games against Detroit.
The teams meet again on Thursday night.
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