Fiala scored twice against his former team, and Devan Dubnyk made 21 saves for the Wild (32-27-8), who are 5-0-2 in their past seven games and lead the Colorado Avalanche by two points for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"That was fun," Fiala said. "But we wanted those two points. We did a good job to get one."
Smith gave the Predators a 1-0 lead at 1:48 of the first period on a rebound in the slot.
Fiala tied it 1-1 at 15:25, deking Predators defenseman P.K. Subban and scoring short side from the left circle. It was the first goal with Minnesota for Fiala, who was acquired in a trade with Nashville for Mikael Granlund on Feb. 25.
"He showed that he's got some pretty good skill," Wild coach Bruce Boudreau said. "They were on display today."
Boyle gave the Predators a 2-1 lead at 13:38 of the second period with a redirection on the power play, but Pontus Aberg scored his first goal with the Wild to tie it 2-2 at 17:49.
Eric Fehr gave Minnesota a 3-2 lead at 2:25 of the third period on a one-timer from the slot, and Josi scored 34 seconds later to tie it 3-3 after he skated down the right wing and cut to his forehand in front.
"I think once I go across the blue line, I try to kind of feel their forward and where he is," Josi said. "If I think I've kind of got a step on him, I try to take it to the net. Sometimes I don't, so I either drop it or try to pull up. I just figured this time I kind of had a step on him and I just tried to put it in the net."
Arvidsson gave the Predators a 4-3 lead at 8:21 on a shot from the right circle that trickled under the right arm of Dubnyk.
"I feel like we have [played a few more games] on all teams," Arvidsson said. "We've got to win here to push for the number one spot against Winnipeg, so we're just trying to win every game and find a good game until the playoffs start."
