Kuemper made five saves in the first, nine in the second, and nine in the third. The rookie's best save came with 2:17 left in the third period when he denied former Wild forward Matt Cullen from just outside of the crease on the right side.
"It's a pretty special feeling right now," Kuemper said. "Obviously, shutouts are always fun and to get one at the highest level is a pretty cool experience."
The Predators have lost three in a row and six of their last seven.
"We tried to force things through people," Nashville coach Barry Trotz said. "Sometimes you have to have to simplify that or it just backfires for you. Full credit to them, they jumped on us."
Heatley scored the game's first goal with 7:57 left in the first period when he redirected Charlie Coyle's shot past Nashville goalie Marek Mazanec.
"I knew we had numbers, but it worked out pretty nice," Heatley said. "We heard from the bench that we had an odd-man rush. (Coyle) made a great play, and that was a pretty easy one."
Former Predator Ryan Suter also assisted on the goal. It was his 300th career NHL point. He has five assists in six career games against his former team.
"They were right there in front of us in the standings and we needed tonight, but we didn't get it," Nashville captain Shea Weber, who was Suter's longtime defensive partner with the Predators, said. "Now we have to move forward and get ready for Calgary."
Nashville concludes a five-game homestand Tuesday night against the Flames.
Zucker doubled the lead just 2:12 later with his third of the season. Heatley skated down the right side with Zucker on a 2-on-1. He sent a pass to Zucker on the left side, where he had an easy tap-in.
Coyle, who had the secondary assist on Zucker's goal, scored twice in Minnesota's home loss to Colorado on Saturday night, giving him a four-point weekend.
"That was an unbelievable response by our guys," Minnesota coach Mike Yeo said. "Winning is ultimately what we're looking for, but how we played the game from start to finish, I mean I have to give big kudos to our leadership group."
At 1:14 of the third, Cooke took a nice feed from Justin Fontaine and beat an out-of-position Mazanec for his sixth goal of the season, and his first since Dec. 5.
Scandella scored with 9:44 remaining with a wrist shot from above the left faceoff circle.
Eight of the 12 defensemen who played in the game were Nashville draft picks, all six Predators plus Minnesota's Ryan Suter and Jonathon Blum. ... Nashville RW Patric Hornqvist returned to the lineup after missing two games with a lower-body injury. ... Minnesota is 2-4-1 in the second half of back-to-back games this season. Wild D Nino Niederreiter has eight points in his last eight games.