Craig Smith scored, and Juuse Saros made 30 saves for Nashville (32-26-8), which was coming off an 8-3 loss to the Edmonton Oilers on Monday and trails the Canucks and Jets by two points.
"We did have a push at the end, but the first period wasn't good at all," Predators captain Roman Josi said. "They were a better team, got off quick. In the third we made a push but took too many penalties … and it's hard to come back from a two-goal deficit.
"We didn't win and we need points right now, so we got to be better."
Luke Kunin, who missed the previous five games because of an upper-body injury, scored off his own rebound in front to give the Wild a 1-0 lead at 4:07 of the first period.
Fiala made it 2-0 at 12:04, skating in on a 2-on-1 before toe-dragging Predators defenseman Ryan Ellis and scoring short side top shelf.
"Fiala's got up for every game as of late," Wild coach Dean Evason said. "I scored six goals a year, so I have no idea (how he does it). It's incredible, it really is. His hands, his vision. He's clearly feeling it."
Zach Parise pushed the lead to 3-0 at 1:38 of the third period when he got to a loose puck at the right post. Parise has six points (three goals, three assists) during a four-game point streak.
Smith cut it to 3-1 at 5:07 with a power-play goal after he gloved down a rebound in the slot and shot over Stalock's glove.
"In my opinion, we outskated them, we outcompeted them," Fiala said. "They got a little life after their goal, that's just how it is. I feel if we play like this, we're going to be dangerous."
