''Everybody is accountable to the way they play,'' Predators coach Peter Laviolette said. ''It was really good to see Craig come back in and play the game that he did today. He had some looks, he used his speed, he's working really hard out there, but it was nice to see him cash in offensively, which he's been able to do for quite a few years now.''
Viktor Arvidsson also scored for the Predators, who have won four of five.
Nashville began the day holding the Western Conference's second wild card, and the victory moved the Predators ahead of idle St. Louis into third place in the Central Division.
Smith, with just nine goals this season, was a healthy scratch in Nashville's previous game Saturday at Carolina. He assisted on both goals by Ellis.
''He's obviously been a little bit snake-bitten for his standards, but to see him get those two points - huge, not only for him, but for our team,'' Ellis said. ''If he can get rolling like he did tonight, it'd be excellent not only for him, but for us.''
Rinne was lightly tested in the first period, making just five saves, but the action picked up after that as the Finn stopped 11 shots in the second and nine in the third. His best sequence came midway through the second, when he denied two attempts by Josh Jooris and one by Jamie McGinn in an 11-second span.
''I thought that even though early on I didn't get a lot of shots, it was still easy to stay in the game,'' Rinne said. ''Just considering the magnitude of this game, it's a big two points and I was treating it as a playoff game.''
Arvidsson scored the game's first goal five minutes into the second period.
The goal was Arvidsson's 27th of the season. Arvidsson has goals in three consecutive games and at least one point in his last five.
''I think both clubs, there was not much going on. Both teams were pretty tight, a tight-checking game,'' Arizona coach Dave Tippett said. ''They got a break on their first goal and we were chasing them from there.''
Ellis doubled the Nashville lead at 16:44 of the second. From the right point, Smith sent a pass to Ellis above the left faceoff circle where he beat Smith with a one-timer high to the glove side.
Ellis also made it 3-0 at 6:35 of the third. Craig Smith carried the puck into the Arizona zone and from near the right boards found Ellis at the right point, where he fired another one-timer by Mike Smith. Ellis has 14 goals and 34 points this season, establishing a career best for the defenseman.
Ekman-Larsson's power-play goal at 16:05 of the third ended Rinne's shutout bid, but Nashville improved to 24-1-5 when leading after two periods.
''We have not been playing with a lot of confidence,'' Ekman-Larsson said. ''It is hard to score goals in this league and when you do not have the confidence with the puck and you do not shoot the puck, you are not going to score and that has been the case the last two games. But it was good to at least get one.''
NOTES: Smith has 201 career points. ... Nashville has defeated the Coyotes six consecutive times at home. ... After spending all season in the AHL, Arizona D Zbynek Michalek appeared in his first NHL game of 2016-17. ... The Coyotes are 5-12-0 against Central Division teams this season.
Coyotes: At the Tampa Bay Lightning on Tuesday.
Predators: Host the Calgary Flames on Thursday.
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