Jamie Benn and Patrick Eaves also scored for the Stars, who moved one point ahead of the East-leading Washington Capitals in the overall standings. Dallas and Washington, which lost on Thursday night, share the league-lead with 28 wins.
Only the Stars, who lost on Tuesday night at Columbus, and the Capitals haven't lost consecutive games this season.
Janmark said his play in December wasn't much different from the first two months of the season despite the statistical difference.
''I just couldn't get the puck in the net,'' he said. ''So, it's nice to get the goals in. If you don't get it, you start doubting yourself.''
Dallas coach Lindy Ruff agreed with his rookie's self-assessment.
''Sometimes, you're in the right place and the goaltender's making a great save on you,'' Ruff said. ''His game for me has been very consistent.''
Janmark's goal came at 17:28 of the second period. The play began with Jason Spezza beating Nashville's Mike Ribeiro to the puck near the Predators' blue line. Spezza skated in on the net and passed across to Janmark, who took the puck off his skate and shot over Pekka Rinne into the net's roof.
That was the first Spezza's two assists.
Craig Smith scored his ninth goal of the season for the Predators in the second period, giving Nashville a lead that lasted about a minute and a half. Smith and Predators coach Peter Laviolette bemoaned Nashville's puck management in neutral ice, particularly when the score was close.
''It's the one thing that we harped,'' Laviolette said. ''The neutral zone was going to be a big thing, and we turned the puck over too much.''
On Benn's goal, he skated in slowly to the right of Rinne with defenseman Ryan Ellis situated between Benn and the net. Ellis dropped to the ice to prevent Benn from passing to Seguin in front of the crease. Benn instead wristed a shot over Ellis and past Rinne's stick side at 12:53 of the second period.
Seguin's goals came at 8:03 and 15:56 of the final period. The first was awarded following a video replay.
''I told Pekka right away, `I'm pretty sure that's in,' " Seguin said. ''He said, `No chance.' But once I saw the replay - actually, I heard the crowd - I knew it was in.''
Smith had given the Predators a 1-0 lead at 11:22 of the period with a backhander that beat Antti Niemi to his stick side.
Rinne, the NHL leader in goaltender minutes, hasn't won on the road since Nov. 5. He's 0-6-2 in away games since then.
The win, coupled with the St. Louis Blues' loss, extended Dallas' lead in the Central Division to nine points. The Stars are 16-4 at home and 7-2-1 against divisional opponents.
''Our talk in training camp has been how we're going to start the year, how we're going to be at home, how we're going to be in our division,'' Seguin said. ''We have a long way to go. But in those statement games, those playoff-type games, we've played really well.''
NOTES: Dallas has hosted a New Year's Eve game for 17 straight years. The franchise is 20-12-3 all time on New Year's Eve, including its previous 35 seasons in Minnesota. ... Shea Weber appeared in his 723rd career game for Nashville. That tied him with Martin Erat for second place behind David Legwand (956). ... Dallas extended a home shutout streak to 167:08 before Smith's goal. ... Nashville's Cody Hodgson was a healthy scratch for the third straight game. . Stars wing Valeri Nichushkin left in the second period with what Ruff called a lower-body injury.