The Coyotes will need to finish the season at least one point ahead of the Stars in the standings since Dallas will hold the first tiebreaker — more regulation and overtime wins — no matter what happens over the course of the final two games.
Dallas hosts St. Louis on Friday. If the Stars win and earn two points, they would clinch the last spot in the West, eliminating the Coyotes.
"It’s not where we want to be," Phoenix defenseman Michael Stone said. "That’s all there is to it really. We didn’t do enough to continue to be able to control our own fate."
Smith scored the game’s first goal at 10:26 of the second period. After taking a pass from defenseman Ryan Ellis above the left circle, Smith skated down to the left faceoff dot, where he used two Coyotes standing in front of goaltender Thomas Greiss as screens and scored his 21st goal of the season with a wrist shot high to the far side.
Smith’s power-play score snapped a 13-game goal-scoring drought.
Hornqvist doubled the Nashville lead at 9:21 of the third. From below the goal line, Mike Fisher found Hornqvist in the slot. Greiss denied Hornqvist’s first attempt, but he poked in his own rebound for his 21st of the season — and seventh goal in his last six games.
"Fish got the puck behind the net and I saw him creeping up the wall," Hornqvist said. "I just tried to get open in the slot. He found me and then I buried the rebound."
The shutout was Rinne’s second of the season and 32nd of his career. He now has 162 wins, moving him past Tomas Vokoun into first place on Nashville’s career wins list.
"We did a really good job of blocking shots and getting the clears when we needed to," Rinne said. "When they got the shots, I was able to see them. It was kind of back to the normal way of game playing."
Rinne missed 51 games this season due to a hip infection.